I also debated this. While we haven't ever used any of these services, we finally decided we'd give gardengrocer a shot. Why?
1 - They charge the least - $12 for delivery ($40 minimum), gratuity optional. Wegoshop is $17 or more + 3% extra for credit payment + 10% gratuity if you're not present for delivery. Goodings is $20 for a $50 minimum order and their prices are reportedly on the high side.
2 - You don't have to be present when they deliver.
3 - It's specifically recommended by The Unofficial Guide.
4 - They will deliver beer (this was confirmed by them in an email just a couple weeks ago).
5 - Their website is very nicely laid out, simple to browse, with most of the foods we would choose at our local store. The only major exception I could find was that they don't carry our preferred coffee. They DO carry tiny bottles of laundry detergent.
6 - Possibly most important, I've NEVER read a poor review for gardengrocer (and I devoted a lot of time to this decision). I imagine there must be a couple floating around out there, but I haven't seen one, and that's a pretty good track record.
To be fair, I have also read glowing reports for wegoshop, and it seems like that's the better choice if you need non-grocery-store items (like an umbrella stroller or a cooler or pharmacy items).