Okay, Edit_XYZ, I think we can go forward based on that. I would just say that:
the way this thread was constructed, it is, almost by definition, an 'inter-fandom pissing contest' between supporters of the 4 captains in the poll.
I don't think this is true. The way this thread is constructed is to chew over a mildly interesting question that probably can't be definitively resolved but is fun as a thought experiment anyway. That's not what I would call a pissing contest -- a pissing contest is what happens when that conversation stops being fun and starts being ill-tempered and hostile. So, thanks for saying that you'll tack away from that.
What I'd like to do is pick several tactical examples for Kirk from TOS and roughly corresponding examples for Archer from ENT to explain my preference for Kirk... and what I said about ENT's nonsensical writing. I'll alternate one with the other.
"Balance of Terror"
-- Ship-to-ship tactics, the great example that I've already cited. There is no third-party interference, there is a convincingly-presented tactical situation, Kirk is confronted by a wily opponent (his tactical match) and uses convincingly-explained methods to defeat him. Unequivocal and well-sold example of brilliant tactical leadership and performance.
-- It was a toss-up between this one and "The Augments" for a fair comparison. This episode is partly compromised by being part of the Temporal Cold War storyline, which on the whole was nonsensical writing at its worst (there was no reason for any of its happening that we didn't have to take the writers' word for, and no apparent reason for the rules governing it than dramatic convenience) -- but tactically speaking, beyond the dubious fact that the Klingons appear to have nothing but Birds of Prey available for a task like this, this episode's action isn't directly
compromised as long as we hold our noses and get past the larger story-arc issues. It's also a clear-cut example of Archer showing real guts and tactical brilliance to work out Duras' weakness and destroy him. For my money, the tactical scenario
isn't as convincingly sold as "Balance of Terror," but nevertheless Archer's leadership is really sold as saving the day (unlike with "The Augments" where he wins with Arik Soong's aid).
Score 1-0 for Kirk. (Both good examples, but Kirk's tactical situation is more convincing and isn't part of anything like the meta-arc TCW silliness.)
"The Corbomite Maneuver"
-- One of two TOS episodes where Kirk bluffs an enemy using the fictional "corbomite device," in my opinion it's the better of the two (the other choice, "The Deadly Years," is somewhat more contrived, requiring a Starfleet flag officer who has somehow reached that rank entirely behind a desk and one of McCoy's many miracle cures). This shows Kirk confronted by an apparently superior enemy, reading and recognizing that the correct analogy to the situation is poker, not chess, and outfacing them until he's able to work out what's going on and expose the true nature and limitations of the Fesarius
"Fight or Flight"
-- The first time we see Archer's vessel in ship-to-ship action. At this point, the NX-01 is still an experimental ship whose weapons haven't even been calibrated (not quite nonsensical writing, just questionable as to why it was let out into deep space in that condition), and that doesn't have the luxury of easy use of transporters. In this situation, the ship is not saved by any inspired action on its captain's part, but by the timely arrival, to put it kindly, of the Axanar; at best it could be called an example of Archer saving the day by diplomacy and/or do-gooding, not an example of tactical brilliance.
Score 2-0 for Kirk, who wins this one at a walk.
"The Doomsday Machine"
-- Confronted by a potential planet-destroying threat, Kirk has to save his ship from the fate that befell the Constellation
while working out a way to destroy the alien device. He and his team work out, with the aid of Commodore Decker's sacrifice and then of his ship, a method of doing it. The scale of the threat makes this more an Odyssey-style contest-with-a-monster episode than an example of ship-to-ship tactics, but it still sells the competency of the crew and particularly of Kirk quite convincingly.
-- The NX-01's confrontation with a doomsday weapon, in this case at the end of a long trek through the Delphic Expanse. Though Enterprise
was making more entertaining television by this point, the Expanse itself and the whole storyline are in this case irretrievably tied up with the nonsensical and contrived Temporal Cold War idea (see above), which this time directly affects the plot in terms of information from Crewman Daniels of the 26th(?) century. Even despite his help, Archer's actions lead to his own capture and the near-annihilation of the Enterprise
(which is saved by the bell at the last second because of an internal disagreement among the Xindi).
Score 3-0 for Kirk.
-- Individual tactics, the classic building-a-primitive-firearm episode (MacGyver before there was MacGyver) to pull out a win against an otherwise superior Gorn opponent. Outside the initial contrivance of the Metrons -- had it not been for the Temporal Cold War, I would have said that Enterprise
deserved praise for not leaning on the god-being trope -- a clear-cut example of tactical skill and resourcefulness on Kirk's part, working with no help, no safety net and no lucky rescues and coming up with a plausibly ingenious solution to his dilemma.
-- The NX-01 lured in by a sinister automated repair station that kidnaps organics. Actually a pretty cool episode as this series went, and again does a decent job of selling Archer's acumen and poise and presents a better reason for the ship to be in this situation than random god-beings. But in terms of the scale of the feat and challenge involved? I think it's evident who the clear winner is.
has the better overall story framing, but for degree-of-difficulty Kirk is the clear winner, bringing his score to 4-0.
That's me putting the four best examples I can think of from TOS against the four best examples I could find from Enterprise