Fat quarters are more convenient because they are precut and you don't have to wait to get your fabric cut. They are like candy, easy to grab a handful on impulse. However, you do pay for that convenience...they are marked up slightly compared to fabric off the bolt.
Some patterns require fabric cut the width of fabric, in which case you need regular 9x44 cuts. I usually buy at least 1/2 yd or more. If it is an especially beautiful fabric that I absolutely love, I have to have at least 3 yards.