Both BSG's carried nukes, while the ENT (foolishly) didn't.
How so? The Romulan War was fought with primitive atomic weapons - making it pretty likely that Archer's "spatial torps" had that type of warhead before he upgraded to antimatter. "Sleeping Dogs" in turn suggests antimatter torps were new to Earthlings at the time, and silver bullets of sorts when delivered to the NX ships; the war might have been fought largely without this tech, especially if it was a brief one.
BSG, nuBSG and ENT missile warheads seem to produce more or less the same magnitude of kaboom. And the effect on starship hull is comparable, too, or at least it sounds comparable when speculated upon in "Minefield".
And the ENT would have problems targeting the maneuverable vipers.
Did NX-01 have targeting problems? The hit rate against all opponents, including the wildly maneuvering Suliban and Xindi, seemed to be the usual 100%.
Of course, output differs radically: the nuBSG anti-craft cannon pump out thousands of rounds to score their hits, while ENT beams lash out relatively seldom. The rate of kills-per-minute still seems more or less the same, though.
What effect would polarizing the hull have with the nu-vipers explosive canon shells?
Difficult to tell - did
Galactica have potent armor when she shrugged off a nuke hit or two? Or just bulk? Archer's ship is less bulky, but seems to be capable of taking the same sort of punishment; BSG small craft never stood a chance against capital ships even in swarms of a hundred, as their missile warheads for some reason never were comparable to those of the capital ships (which is pretty different from the WWII inspiration where aircraft bombs were quite comparable to battleship shells).
On the other hand, ENT's phase canons migth have been able to cut into the Galactica.
Or then the armor that kept Adama alive through at least two nuke hits would also thwart the phase beams. Also, Star Trek engagement ranges are very short, perhaps because phase beams die down rapidly with distance; this would favor
Galactica and her combination of close-in cannon and those missiles with respectable range. Unless, of course, Archer quickly noticed the enemy can't do FTL all that easily, and began aggressively warping in and out - a practice that we know mangles BSG ships to scrap metal fairly quickly.
The two Adamas were very different men.
...But let's assume the reimagined one would be moderated to a close likeness of the original one by the constant meddling of his "better half", the troublesome President Roslin. The scenario does seem to involve a situation where the Cylons are not a pressing issue and actual argument on the bridge may happen.
Most like if the Galactica started firing Archer would turn tail and run (if he was still able).
Running would probably indeed solve this battle, just like in the usual ST vs SW fights: warp drive allows for running while tracking, while jump drives and hyperdrives spell the absolute end of the engagement.
But which side would see the need to fire? Nothing Archer did would appear aggressive to Adama, is my guess: whether NX-01 started hailing, or beaming people aboard the
Galactica, this would take Adama by surprise but would also happen far too rapidly for him to react aggressively before it was too late and dialogue or boarding was already in progress. Ship-courtship rituals in the BSG universe take much longer... And Adama preparing for aggression would be slow and easily observed (launching of fighters, swiveling of cannon, opening of missile hatches).
Timo Saloniemi