I bet most of the guys here will pick the Sigma one.
Using the Sigma 70-300 APO DG myself, so far most of the shots are good when printed on 4R. Some strange out of focus issue though. A little noisy when focusing, but still pretty good value for money telephoto lens!
Couldnt comment on the Canon one because I never use before.
I have used the 75-300 III USM before and i guess you get what you payfor. The focusing is quiet but alittle slow and will hunt if lighitng is not ideal. Also as the front element rotates yu cause use polarisers or gradient filters with it. Acceptable sharpness and colours.