Seems I'm a bit late to this party...
FWIW
That Weaver sits on Painless, my long range 308 as my benchmark for other scopes & rifles. To be fair, I didn't get to do an honest side X side; this was just my thoughts of shooting both at the same distance.
The Sightron SIII was good glass. Without having them together, I would maybe call it a push. What I didn't like about the SIII, it seemed to be particular about relative eye position. Nothing disgusting, but worse than the Weaver; more line the SWFA 3-15.