I have owned the Canon 75-300 USM Mk III. It is not a bad lens, but gets soft between 200-300mm. It depends on your level of tolerance of softness, I guess. I think Tamron is similar in quality, but like so many lenses it may depend on whether you get a good one or bad one off the line. If in doubt, I think it is best to go with Canon when you are planning to use it with EOS unless there is a reason not to. Most of my lenses are Canon except one, a Sigma 15-30, but that is only because the equivalent Canon cost $1000 more. If you want a good zoom range lens all in one, I have heard quite a few good reports about the Tokina 24-200 "superzoom". Granted, it isn't 300mm, so I don't know if it would do the trick for you or not. If you want the sharpest pictures, you could save up and get the Canon 70-200L f4 and add a teleconverter if needed easily with this lens. It is not for everyone, though, and you can still get great results with a cheaper lens. The most important factor of course is your skill, dedication, and creativity...much more important than your lens choice
Hope that helps!