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Observation:
After watching a good chunk of Deep Space Nine, I'm pretty convinced that, if there was some cross universal conflict with the Galactic Empire and the Federation, the Empire would win the vast majority of engagements.
The average Federation ship only weighs in at frigate size for the empire, and Imperial ships are better gunned, better armored, and are swifter at hypserspace.
Trek Feddie ships can more easily jump into FTL, and can even maneuver and fight in FTL speeds, and they do have transporters as well as rather creative officers, but You can't win more than a few battles with such things.
There are ALWAYS more Star Destroyers.

On another note, If the Mandalorians ever fought the Klingons, The Mandalorians would have a tougher than usual fight on their hands. You never hear of good Mandalorian Navy commanders, but the Klingons have quite a few as well as good ships with cloaking devices. What would cripple the Klingons is their love of blades and melee combat as well as their lack of jet packs. All Mandalorians are armored and armed with at least two ranged weapons of one kind or another and while they enjoy a brawl as much as the next warrior, they would certainly do more shooting. Star Wars Blasters have a much higher rate of fire and against the comparatively lightly armored Klingons, Mando Blasters would be devistatingly effective.
I imagine an extremely short, extremely violent conflict culminating in a cease fire in which the Mandalorians offer the Klingons to join them, seeing how passionate of warriors they are as well as having such intriguing technology. That will end in one of three ways: 1. The Klingons accept and Mandalorian Ships become green with big disruptor cannons and cloaking devices; 2. The Klingons decline but accept a more permanent ceasefire; 3. The Klingons refuse. Violently. In this event either the war will be decided by the Mandalorian and Klingon Leaders wiping out bladed implements and settling the war by a one on one duel, or they instantly just go back to shooting each other until either the Mandos Nuke enough Klingons or figure a way to steal Klingon tech or the Klingons win enough Naval Battles to deny the Mandalorians any planetary victory.

Course warp strafing by Star Trek ships is impossible for Star Wars ships to counteract because of the invisibility of warping ships on conventional scanners thanks to speed of light issues.

The Federation doesn't even control 1/8 of the Galaxy.
More like 1/16 -1/20 of it and even that much isnt fully explored and under threat by at least three to four hostile powers.

The Galactic Empire controlled damn near everything short of wild space.

You cant possibly compete with those numbers.

Bigger ships, Bigger numbers, and a Totalitarian government who answers to no one, a situation the Fedderation cant handle.
The Empire has quite a bit in common with the Dominion in that fact. The Federation barely held out against that group and only because the Dominion needed the Bajoran Wormhole to get to the Alpha Quadrant or face a 70 year trip to get there.
The Empire has no such trouble and can reliably move about the Galaxy in a matter of weeks, deploying from anywhere and everywhere with forces strong enough to make even the most stalwart Starfleet commanders soil themselves.
The difference between Star Wars FTL and Star Trek FTL is the difference between the propulsion systems of a modern F-18 and a WWI Sopwith Camel. The Trek FTL system is slower but allows for far greater maneuverability while the Star Wars FTL has much greater range and speed.

The Size thing doesnt seem to bug them terribly, as Star destroyers seem pretty decent at chasing down light freighters.

Star Destroyers have very good linear acceleration, but seem to have very poor maneuverability. They can go fast, so long as they go straight.

Star Trek ships on the other hand are very fast maneuvering and at linear acceleration. In Nemesis we saw a 1.2 km long Reman cruiser make a U turn inside 5 kilometers in under ten seconds. Ironically the fastest U turn acceleration recorded in Star Wars belongs to the Millenium Falcon which accelerated at about 500 m/sec/sec according to analysis of the film Empire Strikes Back. That means, that a Star Trek ship can outrun the Millenium Falcon.

To tell the truth that's not surprising when you know the different types of sublight propulsion used in both universes. A 500 m/sec/sec acceleration is exceptionally good for an ion drive, whereas its nothing more than average for the fission radiation drive system known in Star Trek as Impulse Drive.

I still wonder as to how the Empire would fare against the Imperium of Man. I'm fairly certain the Imperium would dominate ground battles, due to the ridiculous power of the Space Marines. Though the Empire would most likely have control of space.

Keep in mind that Star Wars lasers and Star Trek lasers are different technologies, Star Wars laser weaponry has more in common with plasma cannons or disruptors than real laser weapons.