The Galactic Empire would win: not because of superior numbers (because it doesn’t have those), or better weapons (it doesn’t have those), or a preponderance in mind-wizards with bullshit psychic powers and glowing swords (because it certainly doesn’t have that), but for one reason and one reason only:
For all of the Imperium’s bolters, macro-cannons, cyclonic torpedoes, and virus bombs - for all the endless numbers of the Imperial Guard and the PDF (who will, of course, resist valiantly, before being killed to a man), for all of the unstoppable ranks of the Adeptus Astartes, the Galactic Empire has the ability to cross a galaxy in a matter of days, if not hours, on a basis so reliable that “working class” starship captains like Han Solo can do it on a regular basis. In contrast, the Imperium has The Warp, which is neither fast, reliable, or safe.
Ultimately, this means that for all the Empire’s inferior weaponry, equipment (and possibly numbers, though we have no idea how big the Imperial Army outside of the Stormtrooper Corps is), it has the most important advantages: superior logistics and a smaller decision cycle. If a squadron of ISDs drop over a planet and manage to push past the local defences in place (which, granted, would require a great deal of doing) they’d effectively have uncontested control of space for months, if not years as the Imperium prepares a response which, thanks to the vagaries of The Warp, take decades to arrive, or may arrive three hundred years early, or get eaten by daemons. Likewise, if one of the God-Emperor’s fleets tries to hit an Imperial system, assuming that said fleet is not detected months in advance by some long-range scanner technology which the SW universe has (or which the Empire has reverse-engineered, but more on that later), that fleet would be facing retaliation by possibly a good chunk of the whole Imperial Navy within 24 hours, something which I’m almost certain Imperium naval doctrine would not be prepared for (seeing as most of their enemies use The Warp for travel as well).
End result: The Empire would be able to reinforce and supply its forces faster, and it would be able to respond to situations reliably in days while the Imperium might take anywhere from 300 to -300 years.
On top of that, you have the fact that within the Imperium of Man, technology is religion. The possibility of reverse-engineering hyperdrive in any viable time-frame would be almost nil, because scientific inquiry (as opposed to the replication and refinement of technology) is dead. Unless the Imperium were willing to find a way to rope enough Hereteks (and when is that ever a good idea?) into looking into an Imperial hyperdrive, it’d probably never get done at all.
Palpatine’s empire, in the meantime, is full of scientists: mad scientists, questionably sane scientists, even a few with ironclad rules of ethics. How long before Kamino manages to manages to reverse-engineer a Black Carapace, or Sienar Fleet Systems reproduces a Void Shield? Judging by the, frankly, ridiculous speed at which new engines of war are turned out in the Star Wars universe? Not very long.
Long story short: yes, in a straight up fight, the Imperium of Man would win, hands-down - yet war is not a straight-up fight, and wars are not necessarily won by weapons, but by tactical doctrine, cultural biases, logistical flexibility, and speed.
-And those are the Galactic Empire’s advantages.