At the risk of JoeD responding by saying "Hair Smair, just throw the darn bait in the water and a fish will bite it!" I'm going to try to shorten the response.
I like hair better because there are more varieties, I do love marabou however, it just doesn't last as long and doesn't flair until its still. One thing I always do with marabou is strip it off the main "spine". Unless you're tying the south end of a north bound Wooly Bugger you don't want the end of the jig looking stiff like a paint brush from Sherman Williams.
As far as hair jigs, I will start by saying you need to determine if you are imitating minnows or crayfish. I'm assuming crayfish, so you need something that will last a few fish. For a long lasting jig, I would go with Bucktail, which is the most robust but doesn't have as much action....Squirrel, Raccoon, which is middle of the road, are a good balance of durability and action...and Arctic Fox and Rabbit which have great action. Rabbit also lasts a long time. If rabbit hair was 2" long, it would be my only choice, period. But since rabbit hair is only 1 or so inches long, you either have to palmer it on a shank, or use the strip for a tail (which I don't really like). Right now my choice for best all around is Raccoon, which you can get at some fly shops. See picture below. You can use either the longer guard hairs or the finer diameter under fur for different sized jigs/applications.
On more cool thing about hair is that you can wash it with mild soap and water after use to get all the scum off and it looks brand new for your next trip.