Over 20 years ago, I took some of the fan-favorite literature ("Star Trek Maps" and "Star Trek Spaceflight Chronology", among them, as well as some terminology from fan-made bluerpints and manuals and the like) to form an alternative theory for warp speed.
I assumed that the cylinder-shaped nacelles were "circumfirential warp drive", meaning they housed a single series of warp coils in each nacelle to create the warp envelope. Using Cochrane's Formula from "Star Trek Maps", to calculate warp velocity one takes the warp factor, cubes it, and then modifies the product with Cochrane's variable, which varies in space depending on environmental factors (given TNG's occasional mention of the hazzards of dark matter, I assumed that dark matter and/or dark energy would affect warp speeds). So you cube the warp factor, multiply it be Cochrane's variable, and then by the speed of light, to find how many times the speed of light is in a given area of the galaxy. This would apply to ships in TOS and ENT.
My theory, which I call WDE (Warp Drive Evolution) also calls for the new technology we see from Kirk's refit Enterprise (TMP) forward to be based on a much more advanced warp technology called linear warp drive. Linear warp balances power between two sets of coils in each nacelle (hence the vulnerability to a wormhole effect) to create a warp-within-a-warp effect. The two warp envelopes merge along the axis of motion (some canon ship diagnostic illustrations seem to suggest this, IIRC) to create a fourth-power speed. So Cochrane's Formula from "Maps" becomes a fourth-power formula.
In Franz Joseph's 1975 "Technical Manual", the Constitution-class' warp performance is listed as Warp 6 for maximum safe cruising and Warp 8 for emergencies (full throttle). During "The Cage", the fastest we ever hear Pike order the ship is to Warp 7. Images of the Enterprise from "The Cage" and "Where No Man Has Gone Before" show the nacelles with a different appearance, so perhaps the ship's warp engines (and their capacities) evolved over time with each refit. So perhaps Pike's Enterprise has an emergency speed of only Warp 7. But those warp factors would all be circumfirential (third-power) warp factors.
Since the matter-antimatter reactor aboard Kirk's refit Enterprise (TMP) was obviously more powerful (and much more sensitive to problems, Spock said he was "aware of your engine design difficulties" upon arriving aboard from Vulcan) and the fastest Kirk ordered the refit ship to (in an emergency situation) was only Warp 7, we can assume that the refit Enteprise has a top-end of Linear Warp 7, which would be seven times faster than previously.
This would also chime in with "Elaan of Troyus", in which Spock said that the Klingons' speed was "better than Warp 6"; if the Klingons had linear warp drive first, Linear Warp 4.0 would match the TOS Enterprise at Warp 6.349. Also note that the Stargazer, Picard's old ship with obvious 23rd century technological legacy, used four nacelles. Perhaps each nacelle housed just one set of coils. Also note the Excelsior and Galaxy-class ships (and the Enterprise-C) had a seam running down the length of each nacelle, splitting them in half... to split between two sets of coils?
Linear Warp 6.0 would be the same as Circumfirential Warp 10.9...
Linear Warp 7.0 would be the same as Circumfirential Warp 13.39...
Linear Warp 8.0 would be the same as Circumfirential Warp 16.0...
Linear Warp 9.0 would be the same as Circumfirential Warp 18.72...
Back to Reliant...
If we assume that Reliant is using Linear Warp drive per the notions above, even if she could only cruise at Warp 4 and sprint at Warp 6, she could still be at least as fast as Kirk's TOS Enterprise. If both the TMP Enterprise and the Reliant could cruise at Warp 5 and redline at Warp 7, they could both run circles around TOS-era ships.
