I picked up a copy of Star Trek: Conquest at CompUSA for a steal (what with them going under), and have found it surprisingly enjoyable (though I only do the battles in the Sim mode; I find the Wii controls obnoxious for the 3D stuff). I've figured out some fairly solid strategies, and have completed the campaign as each of the six races (the Romulans are a pain in the ass to play as, but eventually are fun).

I was wondering if anyone knew of another good turn-based strategy game on the 360 or Wii. (preferably the 360, but I'm not picky)

You might try Fire Emblem: Radiant Dawn for the Wii. It's quite a fun turn based strategy game that will mix you up some because your tactics have to change somewhat between the different chapters.

I agree heavily with this but theres a few warnings im going to throw in:
1. Fire emblem is NOT like your normal TBS where you have tons of units to throw at the enemy and die. Instead every unit you have is basically a hero unit, and you don't want to lose ANY of them. This can get hard when some wind up underleveled, so usually you make a team and don't use half the cast unless you replay through.
2.Radiant is considered one of the harder ones due to the lousyness of the early characters and how most of them are useless later in the game. The issue is that since you can only have so many characters you don't really want to wastes exp on characters who don't have much going on for them even when leveled. I'd honestly glance at an faq later if you're going to give it a try.