I like both types. Store bought are more convenient and easier to use for barbecues and parties. There are different types; garden burger where the patty is made up of vegetables and breadcrumbs, or the other where tofu is used. I like them both and usually buy what is on special. Homemade are great to eat, but I don't always have time to make them and I tend to add more potatoes in them to keep them together.
These days lots of cafes come up with black bean burgers or a mushroom burger, so there are more vegetarian burger choices that before. In the UK we have a spicy bean burger by Burger King which is vegetarian approved and they also do a kid's meal with the bean burger.