They both will. They both have good reputations, and it would be hard to go wrong with either. For a typical order, the higher per-item costs at GG tend to be balanced by the higher delivery fee WGS charges. So, the real difference is ordering model. I like the choose-from-a-list model GG uses because it is easier and I am less likely to forget things. Others prefer the write-a-specific-list model that WGS uses because it gives them more control and discretion.
Hard to go wrong, either way.
(Also, GG does the same thing WGS does---if they seem to be fully booked, they won't take more orders for a particular date. So, ordering a bit in advance---a week, maybe a little more---is wise.)