I had a 70-200 f/2.8 and I found that it was too short for outdoor photography. Adding a TC helped, but when I added a 2X it degraded the image too much and a 1.4X still wasn't long enough.
I bought a Sigma 80-400 with OS and used it about a year. In good light, it produced excellent results. It didn't fare as well in poor light. The images were not nearly as sharp as I wanted and it seem to have a difficult time focusing. It was very difficult to shoot birds early or late.
I sold the Sigma and bought a Canon 100-400 with IS. The IS works much better than Sigma's OS, although to be fair, that lens was Sigma's introduction to stabilization and they have probably improved on it since then. I also had a Canon 400mm f/5.6L prime lens. It didn't have IS and it didn't zoom, but it was nice for birds. I decided that the 100-400 was more versatile because of the zoom (even though I'm normally at 400) and it was just as sharp as the prime. I still have the 100-400 and I don't see it going anywhere. The push-pull zooming function took about 30 minutes to get used to, but after that I liked it.
Here are a couple of shots taken with the 100-400 just to show you why I plan on keeping it.
30D - 1/80s f/5.6 at 400.0mm iso500
30D - 1/250s f/5.6 at 400.0mm iso400
30D - 1/30s f/5.6 at 400.0mm iso400 (taken just before sunrise)