cheaper, and 2.8 constant. just make sure you test your copy extremely throughly and make sure it is not a lemon, cos that's the part sigma is bad at. other than that, you are safe with a sigma.
I don't think there's any Canon 70-200mm f/4-5.6 L. For your budget, the closest should be the Canon 70-200mm f/4 L USM (non-IS). Second-hand for that should be around $850 in B&S forum.