Hi Jackie.

Shibori is a Japanese technique of tie-dye, essentially ~ although sometimes it uses other dye-resist techniques like folding, pole-wrapping, or stitching. You can get really intricate patterns through the use of shibori - in fact, I had a friend in college who got major contracts to do huge installations in the lobbies of corporations in shibori. Scroll down on this link:
http://gallery.passion4art.com/members/carol/
and you'll get a sample of the type of patterns you can do with shibori. I haven't been able to find anything on the web of my friend's work, but I'll keep looking.

Batiks are dyed with a wax resist, typically. A lot of mass-marketed batiks are prepared by machine, and they have very regulated patterns. Handpaints are, as you might imagine, hand-painted. There's much more individuality to each piece, but depending on the use you intend to put them to, there's no discernable advantage.

Now you've forced me to commit to catching up to the 2000+ posts I'm behind!