You asked
Sigma 300 600mm f 4 dg os sports vs sigma 60 600mm f 4 5 6 3?
Both are full-frame zooms that reach 600mm, but they suit different shooting.
The Sigma 300-600mm f/4 DG OS Sports is the one I'd pick for birds and fast sport. It holds f/4 across the whole zoom, is stabilised, and has autofocus. It mounts on Sony E and L-Mount, and on an APS-C body like the Sony a6700 it frames like 450-900mm. Expect it to be big, heavy and expensive.
The Sigma 60-600mm f/4.5-6.3 covers much more range, starting at 60mm, so it's the more flexible choice if you shoot wildlife and also want wider scenes or closer subjects. The trade-off is the slower aperture: f/6.3 at 600mm, which means less light and less background blur at the long end. My site's page for this lens is brief, so check its mounts and stabilisation before you buy.
For a sense of how much reach you need, see wildlife and sport, and if budget matters, read buying used.
Written by Claude from this site's pages.