A temporal disruption occurs in the Azure Nebula, apparently caused by a Tholian vessel. However, due to a sirilium explosion destroying the ship generating the temporal anomaly, it not only connects to a point somewhere in the distant past, but in a Galaxy far from the Milky Way. A Romulan Republic Vessel is the first to arrive where they see the arrival of an Imperial Star Destroyer.
The anomaly is stable, allowing the potential arrival of more Star Wars vessels. For the sake of balance, we will limit ourselves to what is seen on-screen for Star Wars and what is capable for Starf;eet, the Klingon Empire and the Romulan Republic/RSE in STO. This does include Star Wars: The Clone Wars animated series.
For the sake of not ending this thread on page 1, let's assume that both sides do not seek to destroy each other at the get-go. We are also going to assume that the humans of the SW galaxy are physiological different from those in the ST galaxy in the way that they are able to use the force. This is for the principle reason that is I take away the force from Star Wars, I need to take something away from Star Trek too.
However, we are going to put a ban an Lord Vader, Emperor Palpatine, Luke Skywalker, etc. showing up on the grounds that the last thing we need is plot-protected characters. I'm also forbidding the use of Q.
In terms of firepower, since it is not stated on-screen, we'll assume the turbolaser weapons are plasma-based (due to the fact that they travel below the speed of light and are much more powerful than an intense infrared beam) with the same firepower of a Gal-X's phaser lance. We'll also assume they have greater shielding to withstand 10-12 shots from a turbolaser barrage of 8 turbolaser turrets (so, 80-96 1-second blasts from a phaser lance or one 80-96 second blast from the phaser lance). However, based on evidence from SW:TCW, SW shields are also vulnerable to projectile weapons (missiles appear to bypass their shields, so torpedoes are the weapon of choice).
The Star Wars hyperdrive will be temporarily nullified due to the Azure Nebula, but is otherwise faster than those of the Star Trek ships, however, the Imperial nav-computers contain no knowledge of the Milky Way galaxy and cannot be used reliably.
Star Trek ships are faster and more manoeuvrable at impulse than an Imperial Star Destroyer, but SW fighters are greater than Star Trek fighters in the same field.
Timeline-wise, Star Wars is dealing with the immediate aftermath of SW:VI.
So, enjoy having a play-around with this idea and let me know if you have any questions.
Oh, and, before someone accuses me of putting ST at a disadvantage due to bias, I'm a Trekkie first.
Also, can we try to keep this civil? Just enjoy the RP experience instead of turning this into a nerd war. Thanks.