Well, Sins and MOO aren't really meant to be compared. Sins is more of a typical RTS with the main victory through conquest. You can ally with other players by doing stuff for them as Brandonv mentioned. You also have to keep doing stuff for them even if you become allies as they keep demanding resources and that they go attack other players.
You can also win through culture. You can spread your culture to neighbouring planets, which weakens the loyalty of that planet and if it hits zero it joins you. The Advent are specialists in this with tech and research geared towards spreading their culture. Personally, I've never bothered as I prefer to blow up everything I can find.
As for the Star Trek mod, that currently only works on the original game. If you have the expansion (Entrenchment) the SoA mod won't work.
If you are looking for a game that is like MOO I suggest getting Galactic Civilisations II. Made by the same people who made Sins and is a 4X turn based strategy game.
That has a range of victory conditions, conquest, alliance, ascension, technology, cultural assimilation...that's it I think.
It has a proper diplomacy system where you can fully trade, made demands, offer treaties.
It has a very expansive tech tree. Which does differ somewhat between the races (I think this only came about in one of the later expansions, probably Twilight).
A more complex economic system where your funds are controlled primarily through taxes from your planets, which you can adjust. You later can research trade technology and the "Galactic Council" can vote on a tax to be placed on foreign planets and starbases within your territory. You can adjust your production spending (normally so you don't spend more as a whole than you get in taxes). You have fleet upkeep costs, building costs (planetary and ship).
It also has a great ship creator. You have standard hulls (small, medium, large, huge) and a lot of parts, which you can then throw together to design your own ships. If you can't be bothered the game always gives you premade ships and all you have to do is swap out their equipment as your technology changes if you don't want to get into creating your own fleet.
You also have random events that occur. Sudden galactic economic turns or "subspace" changes that effect how fast and far a ship can travel. You also have moral events, these events give you choices on how to deal with them, one good, one neutral and one bad. Your moral standing will effect how the AI sees you. Also in the tech tree you can research ethics or something later in the game and once you do you set yourself as "good", "neutral" or "bad". You moral standing up to that point will give you a default opinion. You can choice one of the two others but it costs a lot of cash. Once you made that selection it opens unique research options for that moral choice.
Anyway, that's the basics of the game. It is a great game and if you liked MOO1 and 2 you probably will enjoy GC2. Not sure if there is a total conversion project for Star Trek for GC2 but the official site supports the sharing of ship designs between players and I've seen plenty of Trek inspired designs over there...also seen Battlestar Galactica, Star Wars and even a giant dragon someone made out of the ship parts.
