Since I remember every JS programmer I know uses jQuery. It was my frolic to try MooTools few years ago. I really loved it, and since first use it’s my library of choice. Since I use jQuery a lot, for the team-work sake, let me briefly explain why and when, in my opinion, MooTools is better.
If you are looking for technical differences I advise you to read this great article/page: http://jqueryvsmootools.com/. I am just going to show difference in attitudes and it’s outcomes.