I stayed in Veysonnaz about 5 years ago. Like AiB says, it's a sleepy village with just a few shops. But, the skiing is good and the area is fully connected with the rest of the 4 valleys.
I'm not certain, but I think it took my brother and me about an hour or so to get from the bottom of the lift in Veysonnaz to the top of the mountain in Verbier, cruising at reasonably high speeds on the pistes. That's more an indication of the size of the area, because the lifts and pistes were pretty well laid out.
If you want crazy nightlife and loads of shops and restaurants, then stay in Verbier. If you don't mind a sleepy villages, then take the cheaper option.