jQuery is the most popular js library by a long shot, and likewise jQuery Mobile is shaping up to be a great layer on top of that for mobile. Comparatively Zepto is much smaller, has a smaller API and is still at version 0.8. So why would we use Zepto? First off, zepto is smaller. It’s goal is to stay in the 5 to 10k range. Bandwidth is a much bigger issue on mobile.
One of the things that’s made jQuery so popular is it’s cross browser support, going back to ie6. This is also a big part of the codebase and something Zepto has chosen to pare down. The same browsers aren’t needed for mobile. Since mobile is predominately webkit anyway, you can just progressively enhance for that. If you’re packaging up an app for ios or android this makes sense as well.
Another great thing about Zepto is that it shares syntax with jQuery. The same methods work for both. This leads to a fast learning curve, but more than that. You can start a project in Zepto. If the device requirements change to support windows mobile or you need to use some of the jQuery only methods you can just swap out Zepto for jQuery and your code should essentially work, with only a few exceptions. In conclusion, you should give Zepto a try, but be ready to switch.