It depends. I play exclusively with a pick. I've found that downstrokes give me a heavier sound, more chunky. Alternate picking I use for fast stuff, for smooth stuff, and for intricate left-hand work (just feels better to me to alternate pick when my left hand gets going). Then, to really throw a wrench in this whole thing, we've got a couple riffs where I'll hit the DOWNbeat with an UPstroke. It leaves my pick in a better position to switch to different strings sometimes.
Really, the best answer is do what feels rights. There's not really a wrong answer here...as long as your playing is smooth, consistent, and accurate, you're doing it right.
Warwick Custom Shop Thumb BO 5-string
Schecter Diamond Elite 5-string / Ocean TB75 5-string