Goldbug,
F-107
From what I'm aware of the F-107 was a far better fighter in terms of all around maneuverability. The F-105 was pretty good at high airspeed, but rather unimpressive at lower-speeds due to it's heavy wing-loading.
The F-107's wing-loading were better suited for air-to-air purposes, and it would have had a higher thrust/weight ratio and most-likely better acceleration (at least, it would seem, at lower airspeeds as it flew at a lower AoA)
I'm not sure if it would fly as smoothly on the deck as a lighter wing-loading tends to make for a more rough ride on the deck. Gust response might be higher too (also dependant on wing-loading)
XF8U-III Crusader III / Super Crusader
The XF8U-III, even though it was larger and heavier, actually was roughly as maneuverable as the F8U-2 (After 1962, the basic F8U-2 was called the F-8C, there were sub-variants of the F8U-2 which were designated F-8D and F-8E) in terms of instantaneous agility. It's L/D ratios were similar at typical airspeeds/mach numbers used for dogfighting as well, and it's thrust to weight ratio was at least the same if not higher than the F8U-2's (depending on J-75 variant) which would have resulted in equal if not better sustained agility (the ability to maneuver at a certain rate, or pull a certain G-load without loss of airspeed) than the standard F8U-2. In some respects the plane actually handled better in that the design did not possess a number of undesirable handling quirks the regular F8U/F-8 did. Both airframes were stressed for the same maximum-G load.
Granted it didn't have a gun, but the regular F-8's, even though it had a gun, often didn't use them, or more accurately couldn't -- they were often out of action very quickly as it's guns were unusually prone to jamming under G-load: Of the 19 kills performed in Vietnam, only two kills were performed by guns, the rest were accomplished with AIM-9 Sidewinders or Zuni Rockets. As a result the Super-Crusader would have done pretty much the same so long as dog-fighting training was as emphasized among it's pilots as on the regular Crusader.
Both the XF8U-III and XF4H-1 (What the F-4 was called prior to the 1962 unified service aircraft designation system) had the same combat radius. I'm not sure how the radar's of each aircraft compare, though the XF8U-III's radar and fire-control was said to be highly advanced for it's era.
The XF8U-3 couldn't carry as many AAM-N-6/AIM-7's as could the XF4H-1: The Super Crusader could carry 3, and the Phantom II could carry 4 which did give the XF4H-1 an advantage. The XF8U-3 was, however, a faster aircraft than the XF4H-1, technically it could even outrun the F-106A (Which at high altitudes was a bit faster than even the F-4) and was far more agile -- There was very little comparison in terms of dog-fighting performance to the XF4H-1, the only remote advantage the Phantom had really was that it had a better T/W ratio and would have done better on the vertical (Although this was exploited to it's maximum extent in Vietnam on against the MiG-17's and MiG-21's with great success).
The real drawback of the XF8U-III to the XF4H-1 was it's lack of air-to-ground capability. The Super-Crusader as it was had absolutely no air-to-ground capability built in, where as the Phantom had capacity for up to 16,000 lbs of bombs -- a capacity which exceeded even the Air-Force's F-105. Still, the Super-Crusader almost certainly could have been fitted with wing-pylons to carry bombs as at least some of the regular Crusaders possessed this.
Another complaint that often surfaced was that the plane was a single-seat fighter and as a result, doubts surfaced as to the pilot having a higher work-load during intercepts. The truth was that the cockpit configuration was set up to allow one pilot to manage the work-load in carrying out an intercept -- Chance-Vought even brought an interactive cockpit mock-up to Washington to show that the work-load was manageable (Plus the airplane had a datalink, so it could probably be vectored to a target under ground control much like the USAF's SAGE system did, with the pilot locking up the target, and completing the intercept). Still, I cannot guarantee that the XF4H-1's workload would be lower (And the XF4H-1 did not depend on a datalink) than the XF8U-III's, but I think the XF8U-III was overall a better aircraft (faster, more agile, etc) -- though I suppose having two sets of eyes (with a twin-man crew) would pose some advantages as well.
YF-12A
The YF-12A was built essentially to do what the XF-108 Rapier was supposed to do; perform the role of a long-range interceptor able to operate independent of the USAF's SAGE system with long range radar and missiles. The YF-12A was even faster than the XF-108, with probably at least the same range.
It was based on the A-12 (which was the first of the Blackbird series) with a number of modifications which included the elimination of all radar-absorbent materials, removal of the camera-bay, the chine-bays re-configured to carry missiles, and an enlarged nose to carry the 40" diameter AN/ASG-18 radar, the cockpit enlarged to carry two crew members, and raised to deal with the larger radar and provide adequate over-the-nose visibility.
Originally the airplane was supposed to have a full-chine like the A-12, but the radar and infrared-search and track sensors could not see through it properly, so ultimately the chines were cut back. The raised cockpit and lack of a full-chine required ventral fins to be mounted under each engine with a folding fin mounted under the centerline to provide adequate directional stability.
The AN/ASG-18 and the GAR-9 (Re-designated AIM-47 after 1963) were off the shelf items from the cancelled XF-108, which continued development anyway due to their potential use in nailing low-altitude targets, and ICBM's.
The ASG-18 consisted of a gigantic pulse-doppler radar with a 40" antenna and a range of at least 350 nautical miles. Being pulse-doppler and fitted with a signal filter, it could sift out moving targets from ground-clutter and as a result was a highly-effective look-down/shoot-down system. The radar also could look-up as well and could accurately track an ICBM sufficiently enough to guide a missile into it (making it an effective anti-ballistic missile weapon -- until a few years ago, this was classified). The ASG-18 also included two infrared search and track (IRST) scanners which were slaved in whatever direction the radar was working in (The Air Defense Command was fond of using these kind of radar and IRST combinations, but for an interceptor designed to nail Mach 3+ bombers, it would be extremely useful in that large aircraft that fly at high-speed produce substantial heat-signatures from both kinetic heating and their large engines) and could detect a high-speed target (Mach 3 or greater) from distances approaching (if not exceeding) 100 nautical-miles away.
The GAR-9/AIM-47 was a long ranged delta-finned missile which does not look entirely unlike the AIM-54 Phoenix, and indeed it is a partial-predecessor to it. It is predominantly semi-active with an active-homer for terminal guidance to the target. It can either be guided semi-actively by the aircraft's radar, or fired with the missile flying on autopilot until it's active seeker can acquire the target. It's maximum range is well in excess of 100 nautical miles (the range can under some circumstances be stretched beyond that depending on the altitude and speed of the launching aircraft, and the altitude and speed of the target as long as the radar can successfully illuminate and control the missile -- this applies to all missiles, and is something the modern F-22 actually capitalizes on.). Originally the missile was to be fitted with a 250 kiloton thermonuclear warhead, however by the time the YF-12 was being developed and flown, the missile was fitted with a conventional warhead (though the missile could still be fitted with a thermonuclear warhead). The YF-12A was capable of carrying up to five of these, however the forward right chine-bay was fitted with a variety of test equipment, and probably some parts of the fire-control system installed there which limited capacity to four (one in the forward left bay, one in the rear left and right bay, and one in a center bay behind the main-landing gear).
The YF-12A performance-wise was similar to that of the A-12 in terms of cruise-speed, range and basic handling. Truthfully it was a little bit heavier, it's top end speed slightly lower, with a slight hit in range, but it was not massive. While the YF-12A would never be used in a dogfight, SR-71 pilots have described the airplane (technically the SR-71's a bit heavier than the YF-12A) as behaving similarly to a heavily loaded F-4 Phantom at subsonic speed (though at high AoA, it has a bad pitch-up tendency), with the airframe could pull up to 8g's subsonic, and even the heavily sanitized "technical manual" that has actually been published for the SR-71 does indicate inlet and bypass-door settings and inlet-bias (inlet bias is a term for differential inlet and bypass door settings for each engine inlet due to turns and such) for load factors up to 4g's. As a result it would be logical to conclude the airplane could pull 4G's at high-speed. Considering how large the YF-12A (and SR-71), this is actually quite impressive.
The aircraft proved to be a remarkable success during tests, other than a gyro failure, which sent one missile flying wildly out of control, every missile fired either hit it's target, or would have destroyed the target (one missile missed by 6.5 feet, but the distance was so close that the proximity fuse would have still set off the missile and even with a large conventional warhead, that bomber would have been destroyed), the only two issues the airplane had was that it leaked on the ground and that it was not capable of starting it's own engines.
The first issue they probably were looking into methods of sealing the tanks but apparently that wasn't successful, but apparently the Air Defense Command was willing to look the other way. As for the second requirement, being able to start it's own engines wasn't a requirement per-se, the requirement was that when an interceptor was on alert, the engines must be able to be started quickly, and the airplane able to be taxied to the runway and be ready to takeoff within two minutes of the launch order given.
Regardless the A-12's engines took awhile to get started and for the most part Lockheed and the CIA used two modified Buick Wildcat engines rigged together to drive the engine's compressor shaft up to a sufficient RPM at which it could be started. Lockheed developed a chemical start cartridge that could be fitted to a YF-12A standing on alert and was powerful enough to spin the engine up to a sufficient RPM to get everything going.
Improvements to the radar allowed a partial chine to be fitted to the aircraft, and allowed the central folding-ventral fin to be removed, and careful repositioning of the IRST's allowed them to work mounted on the chine. This production model would have been called the F-12B
Politics really kicked in with this one more so than the F-107, and the XF8U-III. It started and ended with Robert S. McNamara. He was trying to salvage his reputation regarding the F-111 by pitching a modified USAF F-111 as an interceptor. Congress rejected this and forked over 250 million dollars for the first 93 F-12B's. McNamara impounded the money.
Ultimately to force the issue, he actually ordered the large assembly jigs which were used to create large parts for the A-12, YF-12, SR-71 and M-21, destroyed, this pre-maturely ended the Blackbird program, and limited production to 9 A-12A's, 1 A-12B, 3 YF-12A's, 29 SR-71A's, 2 SR-71B's, 2 M-21's, and 1 SR-71C, (which was technically made out of a static test model of the SR-71B, with the rear half of one of the YF-12A's after the tooling was destroyed)