What are the advantages and disadvantages of having landing gear doors? To make comparison easy, let us take the example of B737 and A320, both similar aircrafts with retractable landing gear.

As seen on the photo below, the B737 doesn't have gear doors for the wheels, 



but the A320 does



Obviously, Boeing and Airbus made different choices for the same feature and both seem reasonable. Both aircraft models are well accepted by the airlines.

What are the advantages and disadvantages of both designs?

EDIT: I put links to other images where both aircraft are retracting landing gear after take off. The difference is obvious as we can see the landing gear doors operated for the A320 and no doors for the B737's wheel.
Benefits of gear doors


With gear doors, there are fewer constraints on the retracted gear position. This is especially important in larger aircraft with larger and more complex landing gear. It doesn't need to be flush with fuselage or streamlined (737 also uses hubcaps).
The gear doors provide a good aerodynamic surface
Opening to gear bay can be larger and easier to access


Drawbacks of gear doors


Extra weight for the door and the mechanisms
Extra complexity of opening another door (possibility for things to go wrong)