Depends on what you're shopping for...
I like the string for farmers markets and anywhere else where you'll be walking around and can stuff an empty bag in your pocket or purse and use when necessary. They're really good for odd shaped items. They're not good for box like items though, like cereal boxes, the corners snag on the mesh.
The canvas bags I use for going out for the day and can pack a book, my purse, some snacks and water, etc. I find they're too narrow width wise to put groceries in, and stuff gets squished at the bottom, eg. grapes, soft fruit because they don't stretch like the mesh bags.
I prefer the green "square" shaped bags for boxes and canned goods. They keep them from falling over and everything is tidy and upright at the end of a car ride.