The market is saturated with everybody and their brothers' bit designs that there are tons more alternatives that are even WAY more effective AND less harsh/confusing on the horse than the TT and that can cause less physical harm.
I'm not trying to be difficult, but the bit posted as a European Tom Thumb is actually a full-cheek snaffle. The European TT is a short shank leverage bit that's usually used as part of a double bridle. If you order a TT in Europe, though and you don't tell them that you want it as a single, you'll get something like a Tom Thumb Pehlam. This is a European single TT. The difference is the shorter, more tipped back shank with a little bit of gag movement in the bit to lift the horse's head.
I would still try very hard not to direct rein in any bit that has shanks. When you pull on the rein on a shank bit, the tight side PUSHES the horse's head into a turn. So if you're wanting to turn the horse to the left and you pull on the left rein, the bit is actually pushing his cheek to the right (that's why neckreining works so well in a leverage bit...the rein tightens on the opposite side of the turn and the horse turns away from the tight rein). In a true snaffle, you pull the left rein and the bit pulls through the horse's mouth to the other side. It PULLS his head into the turn from the outside corner, opposite the tight rein. That's why the horse turns TOWARDS the tight rein in a snaffle...the pressure is on the far side of his mouth pulling it inward.
The dogbone in the middle on the black snaffle does make things a little less confusing, but instead of direct reining, if you're transitioning don't pull and hold like you would in a regular snaffle...I'd just give him a little tug, just enough to get the attention on the corner of his mouth and get him listening in that direction and then try the neckrein in that direction.
The black bit also has fixed shanks, unlike the TT. The TTs shanks tip AND swivel, and that really hurts the horse and adds to the confusion. I LOVE the kind of shanks on the black bit there...they only swivel out and don't wind up under the horse's jaw. When they swivel out like that, it allows you to help your horse move laterally, which you don't get in a completely fixed-shank curb. It's kinda like you're opening a door on one side of the horse's mouth when you release pressure from the rein on that side.