We used Garden Grocer for the first time on our last trip (in April) and were quite pleased.
Garden Grocer has an online store that lists the items they have and you choose, knowing the price upfront.
WeGoShop's service is a little different. You give them a list and either tell they where to shop or let them choose where. They are supposed to try and get the best prices on your items.
While I'm not positive, I think that WeGoShop's delivery fee is a little more than Garden Grocer's.
While we chose Garden Grocer, I've heard good things about WeGoShop. I only chose Garden Grocer because I wanted to know ahead of time how much my bill would be. By choosing each item from those available on their website, I was able to do that. Beer, wine and alcohol, while not listed on their site is available. You just type what you want in the special instructions box and someone will call you and arrange for it.
We had never gone to WDW without the use of a car before and I was a little leery of using a grocery service, but was so happy with it we're going to do it again in for our November trip. I think that whichever company you choose, you'll be pleased.