Correct, Star Wars revolves around a Type 2.5ish civilization spanning a galaxy, while Star Trek revolves around a Type 1 to 1.5ish civilization occupying about a tenth of a galaxy.
And yes, averaging around Warp 5 to 7 means the Federation would take longer to deploy across a galaxy than the Republic/Empire would, given how Voyager averaged around Warp 5 to 7 and took years just to cross part of the Milky Way. Warp 9 might be comparable, though.
Things in the Federation’s advantage, though:
The Federation is in the Milky Way galaxy and Star Wars is in the Triangulum galaxy, 3 million lightyears away (per the tie-in between ET: The Extra Terrestrial and Star Wars Episode 1). That means the Federation is in a larger galaxy with potentially more resources, if it could mobilize them.
Federation has a clear technology advantage with matter transporters, better medical technology, and the ability to replicate matter.
The Federation’s ships, while not the kilometer-sized bruisers the Empire uses, are still formidably armed with photon torpedos and phasers, which have a similar power output to the turbolasers of Star Wars. They could pose problems for Star Destroyers and may even win one on one with skilled use of the Federation’s science advantages, but the Federation would be heavily outnumbered by the Imperial fleet if they invaded Imperial space.
The way I see it, due to the -immense distances- involved, either faction invading the other faction’s galaxy would lose, despite the Empire’s superior numbers, FTL speeds, and power generation technology or the Federation’s technological advantages in matter manipulation. Neither side would have the numbers and supply lines needed to cross intergalactic space -and- take and hold territory in the opposing galaxy.
Well there’s also the force to take into factor. While I’m sure people like Picard and crusher would be able to resist jedi mind control, I think worf and Weasly would be susceptible to it. Not to mention the force can guide in flying and help them dodge phasers.