MWD uses loads of cap, makes you 5 x as fast and can be disabled by a warp scrambler (note : not warp disruptor).
AB uses less cap, makes you go approx 2.5 x faster but is not disabled by a warp scrambler.
People sometimes fit both on combat ships so they have the MWD for speed (tackling, chasing) and the AB for menouvering once the enemy has scrambled their MWD.
There is no “better” choice, it depends entirely on the situation. You could fit an AB and end up too slow to catch a kiting target, or you could fit a MWD and end up even slower because the target scrammed you and the MWD didn’t work 
IMPORTANT : Microwarp Drives increase your signature radius by 5x also, making you appear 5 times larger to enemy targeting and tracking. You are much easier to lock, and easier to hit while you have a MWD activated. This can be offset by the extra 5x speed, but it’s a very important factor that should always be remembered when choosing a prop mod.
Welcome to EvE.