What's the competition? And what's your priority: Carrying or competition?
If you're looking to get into something like USPSA or IPSC, then the G34 makes more sense. However, if you're looking at a "reality" based game like IDPA, then you may want to choose a carry gun to shoot with.
I also agree with Creeper and Nathan with this:
the 34 would not be my first choice for full time CCW. As I see it, CCW is the more critical requirement. The 19 is an excellent CCW gun, and you could have fun competing with it... if you discover that competition is really a great thing for you, then you can reevaluate your needs.