In Star Trek, there are some extremely powerful beings who are quite happy to interfere with the physical universe. In Stargate, I don't recall seeing any beings quite like this. Their 'Ascended Ones' have a non-interference policy that is strictly policed.
If there was a mass battle between the two universes, it's possible that the Star Trek characters could beg their 'god beings' for help. We already know about the Q, the Bajoran wormhole prophets and a smattering of others. I'm less certain that the Stargate characters could do the same with the 'Ascended Ones'.
Regarding other major powers, I'd like to see big wars between the two universes. How about Wraith vs. Borg? Replicators vs. Jem'Hadar? Ori vs. Tribbles???!!!
