I can't speak for any of these lenses in detail, however size and weight may be some consideration along with price. With the strong low-light performance of your 5DIII you might consider the f/4 IS version.
It's listed at:
f/4 IS - 76 x 172mm 26.8 oz./760g (about same size but 55g heavier than the non-IS f/4 version)
f/2.8 non-IS (your current lens) 84.6mm x 193.6mm, 1310g (for comparison)
f/2.8 IS II 88.8 x 199mm; 52.6 oz./1490g (just slightly bigger and slightly heavier than the Mark I IS version)
f/4 IS would give you the IS functionality you are looking for, while losing you a stop of light, however you are getting a big upgrade on the size and weight vs. your current lens and as well vs. the other lens you are mainly considering. Price is a decent bit cheaper. While the size difference isn't enormous for most purposes that weight difference is nothing to laugh at, and unless there was a specific requirement for it (which I am sure there are many valid ones out there), I'd go for the lighter, cheaper setup.