I have used both.
I prefer Garden Grocer. More expensive, but much more professional. Items delivered without any hitches. Used them several times. Would use them again in a heartbeat.
WeGoShop - It was nice to have Amy go to more than one store and get exactly what I needed and wanted (more about that in a minute). However, the whole transaction was drama. Before we left home, I sent an updated list within the timeframe specified on the website. Got a call from an exasperated Amy saying it was too close to the delivery date and she had to make special arrangements.
Got another series of calls after we arrived, but we were still on the plane (hadn't turned my phone on). Can't remember what about, but she was, once again, not happy with me.
Arrived at SSR only to find that she had refused to leave our groceries with Disney. So, for some reason we had to remain in our room until WGS dropped off the groceries, because she would only hand them off in person to us (I think it was because there was some wine or other alcohol). So we waited and waited and waited. We called. Come to find out, at some point, they had finally dropped the groceries off with bell service, and never called us. If they were going to drop the groceries off with bell service, why have us wait?
When we finally did get our groceries we got everything we ordered and it was correct, except Amy had added several items that she thought we "might need, but forgot to list"... Ugh!