TTs can be harsh or confusing to the horse if used incorectly or if the horse has a low palate. If you use the TT like a snaffle, two handed pulling to turn or pulling a lot to stop, it can pinch the tougne and twist in the horse's mouth. If the horse has a low palate, it can poke the roof of the mouth with the joint of the mouth piece.
SOME horses, when ridden correctly (one-handed, loose rein) seem to like or prefer TT or broken mouth curb bits. If it works, it works
However, I prefer to try ANY other option myself, lol. Billy Allen mouth or comfort mouth Mylers have a broken mouth piece with limited movement. They lay flatter in the mouth (no port, usually) and have some play, but you don't get that nutcracker action on the tongue or as much confusion. If a horse doesn't seem to like the movement of the bit, I'll try a mullen or low port mouth with swivel or fixed cheeks. Mullen or low-port bits are quite mild (depending on the shanks and length of purchase) and accepted well by most horses that are trained to curb bits.
If you're looking for a transition bit, to go from a snaffle (true snaffle, no shanks) to a western shanked bit, then I like the short shanked, "gag-y" type bits like the tender touch or jr cow-horse bits. I prefer the ones with smooth mouths (no twist or wire wrapped) and a dog bone or life saver (circle piece) in the middle. The double joint helps the bit to lay flatter in the mouth, giving clearer signals. The short shanks allow you to direct rein (pully/plow rein) some while teaching the horse to respond to neck reining.