I would go for a smaller house in Weybridge vs a bigger one in Woking. Weybridge has more atmosphere, whereas in Woking you are either in grand houses or on cookie-cutter estates.
Woking does have a large shopping area, but it's not really that great. I was stuck there for over 2 hours while DD was at a party at The Apple. I was desperate for clothes and determined to come back with something. I ended up buying a pair of shoes, some tights and knickers from a fairly grotty BHS. The downtown area is probably more appealing to teenagers rather than the mature woman.
A lot of people talk up Heathside, but it's just another Surrey comp. A friend was at an interview there recently and withdrew half-way through the day...
We lived for six months in Weybridge when we first moved to the UK, and liked it. We couldn't afford to buy there, though, so moved slightly further west. My kids are at school in Weybridge and they are well acquainted with good public transport links.
If you lived in Weybridge, you would do all your food shopping in the big Tescos at Brooklands or Addlestone, or at Waitrose in Weybridge. From either Woking or Weybridge, you would probably use the giant M&S at Brooklands. I'm not sure where people in Woking do their food shopping - there is a choice of Morrisons, Sainsbury's, Tesco depending on exactly where you live.