I like both Star Wars and Star Trek, but it always seems to me that the tech difference is paradoxical.
The Federation has replicator technology that should make manufacturing fleets of ships trivial, and yet they apparently don't seem to use it. Losing 39 ships at Wolf 359 was apparently considered a massive blow to Starfleet. And then by the time of the Dominion War, there are only like 3 major fleet actions and the Federation only contributes maybe a hundred ships at most. Meanwhile, the Republic and the Separatists were pumping out thousands of ships for a war that only lasted a few years.
Star Wars hyperspace drives are objectively better than warp drive. It would've taken Voyager - a state of the art Federation exploration vessel - 75 years to travel back to Earth. Meanwhile, Star Wars ships can cross the galaxy in a matter of hours.
I don't remember if the faster-than-light communication was depicted in the original trilogy (did Naboo try phoning up the Republic before Amidala went there in person?), but it doesn't matter because again, a messenger can reach anywhere in hours. Whereas in Star Trek, it is regularly a plot point that Federation ships are out of range to talk and would take hours/days (or in the case of Voyager, decades) to reach communication range.
Star Wars has the lead in artificial AI, as the droids are sentient and almost act like real people, and Star Wars seems to have countless different droids. Meanwhile, the Data series (Data, Lore, and Data's daughter) are the only beings a Federation civilian created that have true artificial intelligence, and it seems that nobody else was able to replicate that feat (Data tried with his daughter but her positronic brain broke down a short time after activation).
Star Wars also seems to have the lead in genetic engineering, as the Kaminoan were able to pump out a near identical/perfected copy of Jango Fett, and alter the clones so that they grew rapidly. Clones in Star Trek are very, very rare, and IIRC always seem to be botched.
The Federation seems to lead utility wise, as they can complete makeover people's appearances and make them look near identical to aliens within a few hours in sick bay, and then revert the changes with no scarring. Hyposprays that instantly make you immune to almost everything in Starfleet's database. Also, Phasers being used to blowtorch/weld/melt/light fires/stun people/kill people/disintegrate people. Transporter technology. Incredible sensors that can detect anything from orbit. Also, if you include the Federation's secret banned stuff like their phase cloak that not only turns their ship invisible, but allows it to fly through stuff like asteroids, or their sniper rifle that can see through walls and beam bullets into people's bodies, then yeah the Federation has the edge here. The Federation also has life extension technology that anyone can get.
When comes down to ship to ship combat, it's hard to say, but it seems that the Federation has the upper hand. In the Berman era of Star Trek, Starfleet ships are depicted as being superior to almost anything else. They can catch up to any ship be it at warp or at impulse. Their shields can shrug off anything that isn't a Romulan Warbird, a Dominion ship, or one of those 1%ers like the Borg or the Undine. Starfleet ship phasers are capable of drilling through a planet's crust, blowing up asteroids, and can pretty much destroy any non Romulan or Dominion ship within seconds. Phasers also have pinpoint accuracy and are instantaneous.
As for which option to vote for, I'm going to pick Star Trek Online. STO tech isn't much further than what we saw in the TNG/DS9/Voyager era, but it's more about the scale. The game begins with the Federation being at war with nearly every other power in the setting (Romulans, Klingons, Cardassians, Breen, Borg, Borg, and hundreds of others), and the Federation is seen as holding its ground. It might also be the presentation. In Star Trek, we hardly see fleets of Star Trek ships (just Wolf 359 and those three fleet actions in DS9, and maybe the end of Voyager when they went back to Earth?), but in STO you see fleets of Starfleet ships everywhere (as in NPCs in the missions, not other player characters). Feels like the Federation finally started putting that replicator tech to use.