What are the advantages of a propane grill?
The most often cited advantage of a propane grill is that it takes very little time to get the grill up to temperature for cooking.  Other fuel sources, such as wood pellets or charcoal briquets, do take some prep time before you can start cooking.

Also, cleanup on a propane grill is typically simpler as there is no wood or charcoal left over to clean up.

Many will argue that wood or charcoal gives more of a flavor to the food being cooked.  But, there are remedies to this for propane, including getting what is commonly known as a smoker box to generate smoke flavor.

Ultimately any style of grill can cook very tasty meals.  So it often comes down to personal preference on fuel source.