(As an aside, it's interesting how good a word "raid" is. It's short and sweet. You can use "raider" and "raiding" easily. Compare to "operation".)
TOR raids follow roughly the same formula. There are 5 bosses per raid. One boss will be a "puzzle" boss. The first bosses are reasonably simple in terms of mechanics, while the final fight will be a complex multi-stage fight. There are two or three difficulties: Story, Hard, and Nightmare. Only the first two instances have Nightmare mode, the latest one does not have it. I've only seen Story Mode mode, and I would say that it is definitely harder than LFR, maybe a bit easier than T11 or T12 normal mode.
The step up in difficulty of the last boss is pretty funny if you aren't expecting it. In Eternity Vault, it was a bit like going from a Molten Core boss to Kael'thas in T5. Exaggerating a bit, but it's definitely a large jump in complexity.
Loot-wise, I think TOR's system is much more sensible than WoW's. Hard Mode drops a specific tier of gear. Hard Mode flashpoints drop Tionese, Eternity Vault drops Columni, Karagga's Palace drops Rakata, and Explosive Conflict drops Black Hole. Then Story Mode has gear from the previous tier, except the last Story Mode boss drops current tier gear. Then there's all sorts of commendations flying around, and bits and pieces from each tier can be gotten from specific commendations.
As far as I can tell, Nightmare Mode drops come from a future tier or include mounts, etc. It seems more for challenge or bragging rights.
It is a little complicated with the tokens/commendations, but I find it much simpler than having three levels of gear per tier, and having LFR gear obsolete the previous tier in WoW. It does feel like there's more of a sense of progression, where you move through the tiers as you gear up.
One of the interesting things about TOR is that each player has five companions that they can gear up. So loot that isn't taken by a player is often taken for a companion or stripped for the individual mods that make up the item. This is a lot less waste, and makes gearing up new players easier.
The "puzzle" bosses are a neat twist. This is a boss or event where part of the raid has to solve a simple puzzle. In Eternity Vault it's a very simple pattern matching puzzle, a bit like a Rubik's Cube. In Karagga's Palace it's a Towers of Hanoi puzzle which debuffs the boss. One of the interesting things about these fights is that poor performance on the puzzles is not necessarily a wipe. It makes the fight longer and maybe harder, but still beatable.
TOR does have a raid finder for the first two story modes, but it isn't exactly fully transient the way LFR is. You still get locked out, and then you can only join a group which has bosses that you haven't killed. But you can specify to only join fresh groups which haven't killed anything. The downside of this is that if your raid does break up, it becomes very hard to replace people and finish the instance.
All in all, raiding in The Old Republic is a lot of fun. Five solid bosses with some decent trash makes for a nice two to three hour night. There's a good mix of mechanics and difficulty. The bosses are varied and interesting. The multi-stage final boss fights are a good capstone fight for the instance or the night.
Now, if you don't like raids at all, you probably won't like operations in TOR. But if you do like raiding, TOR's operations are worth checking out.