I think Star Wars factions would beat equivalent Star Trek factions, but they have to win Russian style, with piles and piles of their own dead. I imagine one Star Trek warship would be be worth dozens of Star Wars warships.
Star Trek space weapons almost never miss. Star Wars weapons go quantity over quality, very spray and pray.
A Romulan/Cardassian alliance had about two dozen ships. They had the fire power to hypothetically render a planet uninhabitable to life with a one hour bombardment. No Death Star required.
In Star Trek terms, two dozen warships is a mighty fleet. In Star Wars, two dozen warships is a ragtag force.
Shields on an X-wing or Y-wing wouldn't matter much. Star Trek ships can one-shot any fighter. So you might as well launch a bunch of TIE-fighters.
That's why they hardly ever use fighters except in extremely important military engagements. Star Trek fighters can sometimes dodge enemy fire, but it's still the most dangerous assignment you can get in Starfleet.
If there was a long and drawn out war, I believe Star Wars and Star Trek would merge tactics. The Star Wars groups would gradually implement Star Trek style weapons and the Star Trek groups would gradually build mass fleets.
Hypothetically, if the Star Wars people captured a relatively intact ship, they could reverse engineer the better weapons and shields.
If the Star Trek factions were pushed in a war of attrition, they would stop coddling 99% of their civilians and institute some form of a military draft and also start mass producing ships.