ow, Theo is quite a big guy, and it takes some strength to get him off his forehand and moving forward properly. I've gotten him to the point where it is easy enough to ride him in a snaffle on the flat and over fences, but now that he's ready to move up I'm switching him back to some other bits. I like to switch things up, never letting him get too dull to one bit in particular.
Right now for dressage he goes in either a loose-ring french link or a Myler single-joint eggbutt snaffle, both do just fine.
For jumping I tend to rotate more, between a Dr. Bristol full-cheek snaffle, single-joint pelham (I'd like to replace it with a french link), and a french link 3-ring gag (also called elevator, dutch gag, or Pessoa bits)
For hacking/trail riding/conditioning I use the full-cheek mentioned above, a french link eggbutt, or a square-twist full-cheek depending on how full of himself he's feeling. Also, I use another elevator-type bit on him for jumping and whatnot, it has just a little more control than a snaffle. However I'm not sure exactly what it's called...
I'm thinking about getting a french-link true gag bit for cross-country and upper-level jumping, just for that extra touch he needs sometimes. Especially at competitions where he tends to get more excited.
Also, note that with the elevator bits I always use rubber bit guards because they do have a tendency to pinch lips pretty badly.
Go Eventing!