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Star Trek is superior Pt1

It depends a lot on who is on the offensive, the interpretation of their technology, and which era we are talking about.

The Galactic Empire spanned a large portion of their Galaxy with hundreds of thousands of worlds, not counting the rebel worlds, while the Federation is split between two quadrants of the Milky Way controlling less than a single quadrant with only 150 planets.

Going over some technological fields we can see which one is the more advanced in each area:

1) Artificial Intelligence

Star Trek, as of the 24th century, has only one highly advanced android in existence Data. They are still grappling with the issues of robot intelligence/sentience as of the TNG. On the other hand, they have highly advanced AIs which run most of their ships systems from the bridge and main engineering. They also have the ability to weaponize nanytes.Star Wars has had robots for various functions, from repairs, to mining/hard labor, to assassinations and bounty hunting, for thousands of years. Their robots are largely sentient, have been for thousands of years, and they have had past terminator-style conflicts with their robots according to the expanded universe. Despite having very advanced robotics, the ship systems in Star Wars are manually operated. You can see people assigned at every turret shooting manually in Episode III, and Episode IV on the Death Star. Nanytes do seem to be available in the Star Wars expanded universe as well.My bets are on Star Wars robotics

2) Shields:

Star Trek uses energy shields which operate on a particular modulation. They are effective against both kinetic and energy damage, but if an enemy ship knows the modulation they can bypass the shields. As shields weaken the likelihood of weapon fire penetrating them increases.Star Wars shields seem to be a bit of a mystery, and effective ones are certainly are not portable. In episodes IV-VI, and III, fighters seemed to be able to fly right up to capital class ships and take out their systems. The shield generator for the Death Star, which did repel fighters and other ships, was emplaced on the surface of a planet. During the battle of Endor the Imperial Ships, under orders not to fire, seemed helpless against rebel fighters and capital ships who destroyed significant numbers of their ships, including their flag ship. The shield generators seemed to somehow be outside the shield or something because a wing of fighters were able to fly right up to the shields and destroy them.Moreover in episode V their shields seemed utterly ineffective against asteroids, meaning they might not be able to stop kinetic damage in general.Of course it may also be that shields in Star Wars, which they always call "Deflector Shields" are not the same as shields in the Star Trek sense, and in fact, can only attempt to deflect damage. The shields on Star Wars fighters seem even more useless, as every shot seems to always penetrate them, even energy blasts. In many space engagements rebel and imperial fighters are taken out in one hit.In Star Wars video games, almost universally, kinetic weapons such as torpedoes phase right through shields. A Star Wars fan might object saying most games are EU, and that games were not considered canon, however Disney does consider Star Wars Battlefront to be canon. In Star Wars Battlefront, like in every Star Wars game, missiles, grenades, and kinetic weapons like Tusken rifles go through shields, even portable Droideka shields.In the newest movie Star Wars VII, it was revealed that the shields on Starkiller could not block anything going faster than light. Photon torpedoes in Star Trek move faster than light..... no contest.My bets are on 100% on Star Trek in a battle of shields.

3) Size

Capital ships in Star Wars are much larger than most alpha quadrant ships. An Imperial Star Destroyer has a minimum crew of over 5,000 which is twice as high as the Enterprise's compliment counting civilian passengers.This does create an interesting situation however in regards to maneuverability. A Star Trek ship can successfully meneuver through an asteroid belt, while a Star Wars capital ship has much more problems.