I have heard good things about both the Tamron and Sigma 100-400, and was thinking of getting one myself a few years ago. I was personally leaning toward the Sigma version, but it seems the the camp is pretty much divided between the two brands. Both are about 800$ USD. If you are looking for a birding lens another option is the Sigma 150-600f/5-6.3 DG OS HSM, which is about 1000$ USD. Having said that, my research is about 2-3 years out of date.
I’d love to hear other people’s opinions too!