"Raw firepower > technobabble." I don't think so. I think the situation would be like the conquistadors vs. the Aztecs. While the Aztecs greatly outnumbered the Conquistadors, the latter had better technology. Yes, the Empire has a vast civilization but it was defeated by a group of ragtag rebels in a couple battles, so I think you're greatly underestimating how the Empire would do against a technologically superior (at least in my opinion) military force.
I'm going to be very gentle with this.
1. The Galactic Empire has FTL systems capable of crossing the galaxy within a couple of days, at most. The USS Voyager would have taken 75 years to cover 70,000 light years, which is around half the diameter of a galaxy.
2. The Acclamater-I class troop transport, carried multiple turbolasers that each fired a shot of 200 gigatons of yield. This has been given in the Star Wars:Episode 2 Incredible Cross Sections (SW2ICS). The most generous values for Trek firepower are given in the ST:TNG technical manual, which says that photon torpedoes contain 1.5 kg of antimatter. It seems logical that there would be an equal amount of matter, which would give a yield of 64.3 megatons.
Keep in mind that the Acclamator, which is a troop transport, outguns any Federation starship by a significant margin.
3. Looks aren't everything, you know. Just because Trek ships have a "sleek, modern" feel/look, does not mean that they are more advanced. Also keep in mind the inherent problem with the Federation's AM reactors, which increase reactivity. This is a bad thing, because any competent engineer would design it with minimal reactivity and multiple failsafes. A Fed AM reactor can only be shut-down through ejection, which must be manually activitated.
4. The defeat of the Empire at the hands of the Rebel Alliance was due to numerous factors, and also keep in mind that the Rebels had access to the same technologies that the Empire has. So the Alliance lacked ships, but they did not lack for firepower or durability on a ship-to-ship basis.
Note that the defeat of the Empire at Endor hinged on several, very key factors. First, Palpatine's arrogance played an extremely large role in the defeat; he ordered for the Imperial fleet to launch fighters and disperse their fire on the rebel fleet. The unsupported Imperial fighters were then massacred, and the various Rebel capitals received minimal damage on an individual basis.
In contrast, Ackbar realized that the Executor was the biggest threat, and so had all his ships focus on it. This facilitated the suicide run on the Executor's bridge by the A-Wing. Keep in mind, the bridge shields had been weakened considerably by the bombardment of Ackbar's fleet. Further, the Executor would have recovered, had it not been trapped in the gravity well that the immense mass of the Death Star 2 created. Thus, the Executor crashed into the DS2.
Further, had Palpatine not been obsessed with converting Luke to the Dark Side, the Rebels wouldn't have been able to take out the shield protecting the DS2, and Rogue Squadron and the Millenium Falcon wouldn't have been able to make their attack run on the exposed reactor of the DS2. Keep in mind, however, that DS2's reactor was only exposed because it wasn't finished.
5. It's not Aztecs (GE) vs Conquistadors (UFP). It's Modern US Army (GE) vs a Roman Legion (UFP), only even more heavily biased for the Empire. The Empire has:
25,000 ISDs, as well as many hundreds of thousands to millions of smaller warships.
An economic capacity capable of facilitating the secret construction of the DS2, to a completion of 60% in six months! Keep in mind that the DS2 is, at minimum, 160 kilometers in diameter.
A heavily militarized industrial complex. In other words, combined with the economic capacity, the Empire could churn out warships faster than the Federation could blow them up! And this would allow for a victory by the Empire, even in the miniscule chance that the Federation actually had any possible chance to win.
6. Also, keep in mind that technological superiority only goes so far. I'm not saying that the Federation is more advanced than the Empire (which it isn't). Because even if the Federation's starships were better on an individual basis than the Empire's, the Empire still has far superior strategic mobility with their hyperdrive, and far superior industrial capacity, allowing them to replace warships faster than the Federation is even capable of destroying them.
7. I'm going to say one last thing: I feel sorry for you, that you think that a civilization that has only been a starfaring power for less than four hundred years, and consists of 150 member worlds, could take on a civilization that has existed in various iterations for more than ten thousand years and has more than a million star systems under it's control.