Once upon a time I wrote out all the reasons why I hate TTs....but I can't seem to find that post anymore. So I guess I'll give rewriting it a go.... :)
For me, my dislike of TT's is mostly due to how people around here use them. It's not so much that I literally hate the bit (I've actually ridden a few horses in them with reasonable results - not great/the best, but reasonable), it has more to do with what "the common man" thinks a TT is for and how said person uses any TT they get their hands on.
Around here there are a few misconceptions that very widespread and "common knowledge":
1) TT's are a snaffle with extra "brakes". Just as nice as an o-ring, or any other type of snaffle, just with more stop! Yay!
Um no. The TT is not a snaffle, if you go by the real definition of a snaffle (1:1 pressure ratio).
2) Since a TT is just a snaffle, with brakes, ANYONE can ride in one! They can pull hard on it but since it's a gentle snaffle, no harm, no foul, right?
3) Since a TT is a snaffle, that means it should be direct reined in. Neck reining? What's that? Oh, that's only for people who want to use harsh bits. Psh.
4) Since a TT is a snaffle, it's ok to have one on a very green horse. If the horse bolted with you on the first ride due to fear, obviously pull out the TT and slap it on that horse. A TT is perfectly gentle, just will discourage bolting!
For me, these are the main things I hear on a regular basis when I'm around other horse people. I don't hang around other horse people.
But, I feel like as long as manufacturers manufacture TT's as snaffles, we'll be fighting an uphill battle. I think that until that time happens, TT's really should not be recommended, nor should they be used by anyone uneducated about their purpose.
And, on top of that, if your horse functions best in a curb, most of the time there is 100% a curb out there that your horse will accept better than he/she will accept a TT. Sure, you might have to look for a while and try many different bits but I guarantee you that there is something out there that your horse likes just as well, or better than a TT.
To comment on your comment about TT's looking like other curbs you've seen, sometimes they do. Usually it's a difference of a swept back shank (more pre-warning for the horse before bit action happens) or something else like that.
Personally, I do not like broken curb bits as a general rule. I much prefer a slightly ported mouth, no breaks. I don't like how broken bits can pinch and I feel like that's a lot for a horse to have going on in it's mouth - broken links, curb chain, lots of things.
Some horses do go well in a broken curb but I very much prefer a more solid mouth for my horses.
Basically, it's not that the TT is a bit made of the devil. It's the lack of education surrounding the bit and the prevalence of other, better, bit options.
For me, it's like choosing to eat jelly beans for dessert at a 5 star restaurant when you could have had the restaurant's award winning, world class,....some fancy dessert... you know?