Well... I like them both.
It is really hard to name a favourite, because there are great games in both areas.
I would dare to say there are more RTS games, and they usually focus on the Multiplayer, while TBS games seem to be more Singleplayer oriented.
If I would have to choose one genre, it would be RTS. Stronghold Crusader, The Battle for Middle-earth, Starcraft, I had so much fun with them, endless hours of training, winning and getting my a** kicked, it is just great!

I love both, but my vote goes to RTS.
I just love the non-stop action and split second decisions in games like C&C, Company of Heroes, Sid Meier's Gettysburg!, and Supreme Commander.
I'm not really good at any of them, but I don't really care. They are fun!

Always thought RTS's were the games i loved, but after trying TBS's... never looked back...

I like some RTS games, but not all. I prefer ones that focus less on building things and more on (somewhat) effectively using my units. Because of this, my two favorites are Company of Heroes and Dawn of War. I'm also fond of Halo Wars, which is incredibly simple but, in my opinion, more fun because of that. I don't like RTS games in the vein of Age of Empires or Empire Earth. I was able to have some fun with Age of Empires, but overall these types of RTS games just don't click with me.

As for TBS, I love the idea behind them, but I often find it difficult to actually enjoy the games. Granted, I haven't tried very many (Galactic Civilizations II demo and Alpha Centauri being the two major ones), but my experiences with them have been quite similar. My main problem with TBS is that I never feel like I'm playing it right, a problem I don't have with any other genre. I usually start to feel like I'm rushing through everything. This causes me to slow down and obsess over every detail, and then when things don't change, I start to wonder if I'm missing something important. It's annoying because I really want to enjoy TBS, but I just can't get past that feeling that I don't know what I'm doing. That said, I don't foresee giving up on the genre. Every once in a while I'll go back to one of the TBS games that I have, and maybe one day I'll find one that just clicks with me.

I don't like TBS games at all, because they take too much of my time. Then again, Total Annihilation is an RTS that also takes a lot of time, but it's not really my favourite RTS. Those would be Red Alert, Age of Empires 2 and Dark Reign.

RTS games make me anxious, I don't have fun playing them.

I like a good TBS game though, especially when it's an RPG or something like that at heart.

Used to be RTS nowadays it's TBS. But I would still play either.

I like old TBS games, newer ones annoy me with their lack of hot-seat play.
For RTS games I prefer the base building ones over the small squad ones.

In a pinch I'd probably say I like TBS more because it lets me play at my own pace.

Both have their merits. RTS is about thinking on your feet, TBS is more like chess move and countermove.

Yeah, kind of how I think, except I think it would actually be nice to have some way to have time pressure in TBS games, like there is in chess.

To answer the question, I usually pick the type of game depending on my mood (like everyone else, I bet), but I like both types. RTS games are quite fun when you play them with other people.

RTS all the way. Base-building ones are the best, but squad-based ones are good too. I just think they are more exciting and far less time consuming. In the time it takes to do one turn in the later stages of a TBS you could get in a whole match of Starcraft.

Not that TBS games have no merit, I actually like them in general. I just find that they get pretty tedious, especially towards the end of a match.

Mines is turn based. Although i do love the rush of an rts i prefer the tactical element you can have with tbs.

I started with TBS and stayed with them.
Never played a RTS cause for me every one looks like using the same *strategy*...
building your base, collect material for a better base and more units, some minor battles, till finally all in, a massive battle.
Not very strategical for me.

I love turn based strat games , used to be a huge rts fan but its kinda limits your freedom to have fun in the game specially when opponents just rush in early asap to kill off.

at least in turn based you can relax and think over a bit without worrying that your base will be burned down within minutes of the game start.