It's partly going to depend on what type of turning you do as to which route will best serve you.
The sand, as it's many small particles, will dampen vibration far better. The granite, where as it's a solid object, is going to have far less dampening ability and only really add weight, which will help with adding mass to stabilize the lathe while turning large, out-of-balance pieces.
If you are going to turn long, thin spindles, which will benefit more from vibration damping than adding mass, go with sand.
If you are going to be turning big bowls and other large, off-balance face grain turnings that will benefit more from mass than vibration damping, go with the granite.
Having turned my fair share of both, I prefer a (full size) lathe at least 500lbs in weight, my current weighing 650lbs, and my ballast of choice is sand.
If you are going to use the granite, which I'm not against in any way, fill the voids with sand, as this will still help a bit with vibration damping.
And build the stand as beefy and overbuilt as you possibly can, think bomb-proof.
I have seen what appeared to be a very nice stand loosen up in just a few months when only built with construction lumber, plywood and deck-screws. Lathe stands really benefit from hardwood, strong joinery, large bolts and other beefy hardware.
Good luck, be sure to post some pics when you're done!
PS: Thanks for the idea on the sink cut-outs! I've been wanting some nice granite for a sharpening station, and a sink cut-out would be perfect! Really an awesome idea, thanks so much, I never would have thought of that!