Both are reputable agencies and have devoted customers. There are some basic differences in their styles.
Garden Grocer: You shop a "virtual" grocery store and pick items to add to your list. I believe the prices are marked up a bit. They have a minimum order amount. They offer free delivery if the order is over $200. Their delivery window is 2 hours.
Wegoshop: You make your own list of items (including Brand Names and sizes) and Email it to them. They will shop where you request, there is no item mark up - they give you the grocery store receipt. Their delivery fee on our last visit was $17. Their delivery window is 30 minutes.
We have used wegoshop.com 5 times and will use them again in the future. We have been delighted with their service. I prefer to write my own list of what I want and specific whether or not I will allow substitutions. I LOVE the 30 minute delivery window. We have compared and we have always saved over shopping at Disney. We order breakfast items, juice, coffee, fruit, water, soda, beer, wine, cheese and crackers, and some snacks.
I highly recommend them