Please don't make this a Trek vs Wars thing. That is not my intention.
Not looking at any technological or Jedi factors, I was wondering about a Star Wars in Star Trek kind of encounter. Distill Star Wars (Rebellion Era) and you get a few big features that fit into Star Trek pretty interestingly. You have a large, oppressive Empire and you have a Rebellion fighting it for democracy and freedom. In respect to Star Trek, what would be interesting ways to introduce this region? How would Star Fleet (TNG era hands-off) react under each scenario?
Some scenario ideas...
1. The Star Fleet vessel encounters the Empire first. They are large, powerful, and might be good allies against the classic enemies of the Federation and would definitely be good to trade and exchange with. Only later do they find out that the Empire is racist against non-humans and is crushing freedom and free thought. How would this play out with Capt Picard? Star Fleet in general?
2. The Star Fleet vessel encounters the Rebellion first. They are being pursued by an Imperial battle fleet and request the help of the Star Fleet vessel. They are clearly outmatched without help. Again, what would the Picard-like captain do? How would this impact relations with the two new factions they've met?
3. The Star Fleet vessel encounters the Rebellion first. These people are not actively fighting and don't mention the fight against the Empire, but instead talk optimistically about their great Republic that's fallen on hard times. The Federation establishes friendly relations and sends non-military aid. Only then does the Empire find their little enclave at the edge of their space and attack in force. How does the Federation react? Send non-military aid to a friendly nation? Send military aid to an ally? Attempt to pull both parties into peaceful arbitration? Withdraw from the region and cease relations with both parties after discovering the illegal nature of the Rebellion? Secretly support the Rebellion against the Empire and provide non-tracable assistance behind closed doors but denounce them in public?
4. Star Fleet meets the Empire first. Relations are initially good but then the Empire tells the Federation about a pesky Rebellion trying to overthrow the established government. How would the Federation handle this?
5. Star Fleet meets the Empire first. Relations are initially good but then a Rebel fleet attacks the Empire while a Star Fleet ship or other Federation representative is present. The Empire has no trouble proving they are the official government of the region and mentions the Rebellion wants to overthrow them but has been little more than a nuisance so far. Despite this, the carnage from the Rebel attack is great. How would the Federation react?
I think the large scale interaction of such a non-Trek set of political forces with traditional Trek political forces would provide for some interesting and unexpected changes to the normal game. There may have been small scale versions of this in various episodes (the Ansatia separatists/rebels for example) but this really hasn't been done in large scale as a full arc in exactly this way (the Ansatia rebels took innocent hostages and destroyed non-Imperial property to get attention while the Rebellion of Star Wars was shown very differently, only intent on striking directly against the Empire).
Please feel free to expand my sample scenarios and discuss them to your hearts' content within the political theater. Stay out of technology and Jedi-in-Trek discussion. For my part, I'm thinking only of the Federation, Star Fleet, and Captain Picard of the first three seasons of TNG. During the life of Star Trek, the official vision of Federation and Star Fleet policy and politics changed a lot, and the other captains don't fit my view of this era of Trek philosophically. If you are assuming any differently in your discussion, first try not to but if you must then make sure you explain which Trek style you are using as a basis and explain how the differences between my Trek and yours would play a part, if you can. Thanks.
Editted: more scenarios