where do i fucking begin. the rebuplic HAD VIRTUALLY NO ARMED FORCES. THE CLONE ARMY WAS AT ABOUT THREE MILLION AT IT'S HIGHEST.
besides, only the empire and other forces that use warp travel (the tau don't i think, neither do the tyranids) enter teh galaxy, because if you're not in another dimension then you won't be able to get through the storm of gravity and gases and dark matter that surrounds the galaxy star wars is set in.
and if we assume that the force is actually what is canon and not what is displayed in the movies then it is equal to chaos at least.
they would lose before they could say "hey, what's that ominous spiky ship that entered the system?"
but if they attacked the empire that followed after teh fall of the republic, things would be different. the stormtrooper armor is about equal to imperial guard armor exept it covers the whole body, the imperial armored vehicle units is in the end about equal to the imperial(40k) tanks and such. when it comes to numbers, the empire(40k) is only a part of the galaxy, the empire(star wars) is the entire thing. it forces people into service. having countless sodliers from countless races at it's command.
and the empire has ships that rival the size of the ships displayed in teh video and more. an example is the super star destroyer.
it's just so much to go into. basicly, it's an even fight if you don't include infighting between orcs chaos space marines and imperial guard.