Sigma 70-200 2.8 HSM II (non-OS) and Tamron 70-300 USD VC

Between the 2 lenses (Canon non IS vs Sigma non OS), even though the Canon is slower I'd go for the Canon. It's just a better lens all the way around in terms of IQ. Unless you just absolutely positively need an f2.8, I'd say f4 will suffice in many settings.

I've got the Sigma 70-200 f2.8 OS and love it. It's a complete optical redesign next to the previous generation. I just couldn't do a lens of that length without having some sort of stabilization - at least the way I use it. Stabilization is great even with a fast lens - and super-essential if your shutter speed drops into the double digits. You won't be able to freeze a fast moving subject, only a high shutter speed can do that - sometimes facilitated by a wide aperture. For me, I couldn't take advantage of f2.8 in say, a concert setting without stabilization - I'd need a tripod to get a decent keeper rate.

I also had the Tamron 70-300 for a little over a month - 4 versions actually. I couldn't get a decent copy. However, the VC was nothing short of amazing for a lens of that cost. For outdoor use I'd highly recommend it. Sharp and fast AF along with a nice size and good handling could make it a winner with a functioning copy. However, as good as the VC was, my low-light indoor shots were never as good as the Sigma. But for semi-decent ambient light it did quite well, and I could easily stop down to 1/30 and even below. Look back to around July for loads of samples I took on this forum.

I guess it boils down to what the majority of your shooting is. Perhaps renting/borrowing a copy of what you're considering might help you towards a decision.