Quality in craftsmanship and design. If you're just getting a plastic tournament set or a modest wood set, it doesn't matter. If you're going to spend a wad of dough on a nice set, though, there's no reason not to get Staunton.
The main reason they're the be all and end all for the cheaper sets is advertising and sponsorship.
Why is Staunton the be all and end all in chess sets?
And why so pricey??