the 12-24 is a stop slower, but it's a very good, solidly sharp lens with a lot more focal range. It's equiv to like 18-36mm (Nikon) or 19-28mm (Canon) or so on a full frame, so it gives you everything from slightly wide of standard, to ultra wide angle. (think of it as similar to something like the 17-40 F4L on a 5D but, with slightly less focal range) The distortion isn't too bad, a little barrel at the wide end and minor pincushion at 24mm, but overall, pretty simple distortion that can be easily corrected, or just ignored since it really isn't that bad. Ultimately, the big thing about this lens is that it's a very good, well constructed lens with great optics and it costs around 300-350$ used depending on the condition...
The 11-16 f2.8 is faster, better in low light situations, but it's also like having a ~16-24mm (Nikon) or ~17-25mm (Canon) - so you really only have wide angle focal length options. It's extremely low distortion, super high quality glass, very sharp (sharper than the 12-24, but only just), and it's really the only thing of it's kind out there. That said, it also costs about 150-200$ more than the 12-24, doesn't give you a ton of focal range, is, at least from what I can tell, almost exactly the same size/weight, and is far more of a special purpose lens for ultrawide applications.
Personally, I would not want to just walk around with the 11-16 almost ever, but if I was predominantly shooting sports, using wide angles, or shooting a lot of followcams, I'd absolutely love one.
on the contrary, I would much much rather have the 12-24, because it contains a longer, more practical focal range, still keeps a constant aperture of F4, and really doesn't have any worse optics once stopped down (the 11-16 is better performing at the 12-24's maximum of F4)
Ultimately, if I'm doing followcams, for almost any sport, I'm not going to want to be using anything greater than F5.6, because I'd rather have the flexibility of a deeper depth of field for maintaining focus. Therefore, having a faster lens wouldn't really mean a whole lot to me unless I was shooting followcams at night - which I really don't see myself doing too often. The extra width that you get out of the 11-16 also doesn't matter, because the wide end on either of these is beyond wide enough for almost any application. Having the ability to shoot with a tighter field of view without needing to change lenses is also very nice.
On top of that, the 11-16 pairs much better with Crop sensor lenses, like the 17-50's out there, while the 12-24 pairs with any 24-70, or 24-100+ lens you can find, which are going to work on full frame if you ever plan to switch, as well as give you a longer focal range to use.
Ultimately, you can't go too wrong with either of these, they're both fantastic lenses. I just think the 12-24 is more practical and cost effective than the 11-16. If I wasn't shooting on Full frame, I'd hands down have something like a 7D, a 12-24, and a 24-105L and keep it at that. (with nikon, probably a D7000, a 12-24, and a 24-120 F4)
Have a nice day, Bluename.