Is the first bit a tom thumb? I've heard pretty bad things about them... I guess they don't give the horse enough warning before they start acting or something... Here's an article that explains it pretty well: Trouble with Tom Thumb
Tom Thumbs were the main bit (until we started switching them over to snaffles) we used at my camp and there was only one horse (out of 15) that actually went better in a TT than a snaffle. I would definitely start him in the snaffle and if you decide to move up to a shanked bit eventually, find one that isn't broken in the middle (like a normal curb)... I'm not very good with western bits... If the chin strap is what you need, a normal curb bit should be able to have the chin strap and be gentler on his mouth. Good luck!