This depends on the flavor that you are looking for. A grill does not use charcoal which means the resultant flavor is much less smoky. If you are looking for a healthier burger, a grill will be better for you. The griddle will not allow the fats to drain off, meaning that your burgers will cook in their own juices. This will give you a more flavorful and moist burger with that classic grilled crust on the outside.
The heat of a grill can be inconsistent across the surface, particularly if it is not a flat top. This can result in your burgers being undercooked in the center or unevenly cooked throughout. A griddle has a consistent temperature across the surface, giving you the perfect conditions for cooking a burger patty.
Griddles also allow you more flexibility with building your finished burger and incorporating toppings. The surface allows you to caramelize onions while the burger is cooking, meaning that the entire thing is ready at the same time.