United Federation of Planets VS Galactic Empire
This particular debate has been going on since the dawn of the Internet. Today I'd like to offer my point of view on this topic. First some rules are needed:
1.NO time travel science for the UFP
2.NO nonsensical data from star wars such as immense firepower or acceleration
If those are settled then we can get to business.
TERRITORY/POPULATION SIZE
The Empire spans across a significant proportion of the star wars galaxy which is about 100,000(canon)-120,000(legend) light years in diameter with about a million inhabitable systems. The imperial senate consists of at least 4000 senators with a rough maximum of 5000 during the imperial era. The population of the Empire can easily reach 50 trillion.
The UFP controls about a quarter of the galaxy spreading across 8,000 light years with about 150 member worlds. It contains about a thousand inhabited systems with a total population of about a trillion(about the same as the population of Coruscant).
Winner: Galactic Empire
SPEED
FTL
The Empire can travel across the galaxy in days shown in both canon and legend while Star Trek ships require years to crawl across a quadrant of the galaxy.This means that if the Empire invades the UFP then it can jump out of hyperspace, destroyer a target, have a cup of coffee while the navicomputer calculates its next destination and jump back into hyperspace while the federation is still trying to warp toward the place.
STL
Federation ships are shown to accelerate and travel at speed much faster than any imperial ships. Although some star wars sources suggest ship accelerations of 2300G for star destroyers this is clearly untrue as we've never seen any star destroyer travelling at that speed.If somehow UFP ships caught up with the imperials the star destroyers will have a hard time dealing with UFP ships that can literally run circles around them.
Winner:No winner. The Empire may have superior FTL technology but the Federation is much better at STL maneuvering.
MILITARY SIZE
TROOP COUNT
The Empire has way more troops than the federation. There could be tens of billions of stormtroopers alone(not to mention other types of troopers) stationed across the Empire, the red shirts will pale in comparison to that. If you take out the numerical advantage from the empire then you've got a pretty equal match.
Stormtroopers are a group of elite soldiers that are deployed by the Empire to do the dirty fighting and crush any resistance.They are totally obedient and are trained to fight regardless of their lives. Their greatest weakness is their unstable performance. On one hand they were said to be the best and most feared soldiers in the galaxy;on the other hand they were unable to aim properly or to kill a small band of rebels(as shown in ANH,TESB and ROTJ)and are being slaughtered by intelligent teddy bears on the Endor moon.
Red shirts are pretty much the same thing.They are deployed from star ships and often die in large numbers just to show how great the enemy is or how good the main characters are.Some UFP soldiers are actually very skilled in combat techniques, this is also true for certain imperials such as the 501st legion.
Winner:Empire(due to size)but if its a 1v1 situation then its a tie.
GROUND COMBAT
The UFP utilizes ground forces equipped with all sorts of phasers, photon grenades and also ground vehicles to an extent. Star Trek battles don't usually have their major battles on planet surfaces but rather in space so we don't know if there are more weaponry.It should be noted that UFP soldiers are actually very good as shown in certain ground scenes.
The Empire,on the other hand,possesses an incredible variety of ground vehicles from repulsorlift tanks to different kinds of walkers.The most known ones are the AT-ATs and AT-STs. They all have powerful laser canons and/or blasters and heavy armor plates(although AT-STs have questionable armors as seen in ROTJ).The Imperial Army possesses different kinds of ground troops that can fight in almost every environment which means that they will gain the upper hand if battling UFP ground forces in extreme environments thanks to the variety of equipment gears.
Winner: Empire.The UFP would lose almost every ground battle against the Empire.
NAVY COUNT
The Empire is said to have millions of star ships in which there are 25,000 imperial class star destroyers, dozens of dreadnoughts and possibly hundreds of millions of fighters(Which some are stupidly designed and unshielded).The Empire also possesses several battle stations(In ANH, han commented on the death star as being too big for a battle station which implies that there are other battle stations).There are known to be navys station across the Empire for repair and refueling.The Empire also had three world crafts under construction orbiting Coruscant.
The UFP star ships range in the thousands with BIG fighters. They too have space stations and artificial worlds as shown in Star Trek:Beyond.