One excellent infant/junior school in Weybridge which has stiff competition. Others are also quite well thought of, I believe. Good secondary school, probably the best in Elmbridge Borough Council (state school, that is). Don't know what the schools are like in Woking, although we briefly looked at secondaries there.
Woking has some pretty areas around it, also the theatre, cinema etc but the shopping centre is a bit limited. Not to say Weybridge isn't, but it's a different kettle of fish, so to speak.
Fast line to London from Woking, but it's nearer from Weybridge so you don't gain a huge amount.
It depends on what you want from the place you live in. We're in Weybridge, rarely go to Woking for shopping, we tend to go up the A3 to Kingston.
We actually had pretty much the same dilemma as you and (as you can see) plumped for Weybridge in the end, mainly because of the secondary school. But then again, given the chance of a bigger house...