Gator board is very well known for its durability. Thanks to it’s denser foam it makes any display water resistant and would withstand outdoor weather in most cases.
Foam board makes for a finer finish making it a good option for a professional display. This option would be best used for weddings, images, presentations, ect.
Once you tell us what the intent use of your mounted image will be for we will then determine what would be the best route to go with.