Fixed wing drones have a much greater range and endurance compared to the multi rotor platforms.  They do however require more space to opperate.  These are great for mapping type applications where you need to cover a large area.  Also a great if you want to fly FPV (first person video) where you stream a video onboard the drone back to the ground.

Multi-rotor Drones are great if you live in an area that does not have as much open space.  The most common type of multi-rotor is a quadcopter (4 motors).  These type of platforms are ideal for aerial photography type applications as they can hover in specific locations to take photos of objects or areas.  The main dis-advantage is that the flight time of multi-rotors is limited compared to that of fixed wing drones.