Having used both - it seems to me that Prototype has more utility functions for working with various types in Javascript (its many string helper functions come to mind). jQuery's power seems to lie in its very robust selector engine as well as the method chaining. Further, I find that jQuery's event model seems to make more sense to me, and I also quite like the fact that you can store arbitrary objects using the .data() api. Finally, the plugin community is much richer for jQuery, and I usually find that there's a plugin out there somewhere that does exactly what I want.
In short, I typically use jQuery for all javascript development tasks these days. I do find that Scriptaculous (built on prototype) is very nice though. jQuery UI is catching up quickly though.