Worth upgrading ?

Hello everyone,

I’m considering upgrading my lens, a Tamron SP 200-500mm f5.6 (Model 31A). I’m looking at the Sigma 50-500mm f4-6.3 EX APO. Firstly is the auto focus worth it (lens used for wildlife) ? Reviews I’ve read say that at f6.3 the auto focus is slow or useless in all but direct sunlight. My current lens is a constant f5.6 throughout the range. Secondly are the optics any better ? Is it worth spending the £600+ ?? Any thoughts are welcome, thanks.