I'm obviously a jQuery nut, but I can appreciate prototype as well (and have used it more than a few times).
Prototype's approach is to replace the repetitive code you write most often with shortcuts, like replacing "document.getElementById()" with "$()" and smoothing out the process of getting form values with the "$F()" function.
Another strength of prototype is that it's well supported by other projects, likely since it was the first good, widely used javascript framework. Ruby on Rails integrates tightly with prototype, and includes it by default. Scriptaculous is based on prototype as well.
The final attribute of prototype that many people value is that it still smells like old-fashioned DOM scripting. You do everything the exact same way you always have, except now you type less. It's a very comfortable transition for old-school DOM scripters.
jQuery takes sort of a sideways approach to DOM scripting (but a welcome on IMO). Instead of just giving you shortcuts to commands like "document.getElementById()" (which it does, sort of) it applies the theory that what you really want to do is to find stuff, then do things to/with it.
Half of jQuery is just matching elements on your page and giving them special methods. One of the things that you may find helpful is that you match these elements with CSS3 selectors, which (chances are) you already know. To hide all the h1 elements on a page you simply need to write: "$('h1').hide();" - jQuery finds all the elements that match the selector "h1" and applies the hide() method to them.
Another nice thing about jQuery is that it's chainable, which saves you from having to match elements again and again: "$('p').append(', yo').addClass('cool');" - adds ", yo" to the end of every paragraph and then adds the "cool" class to every paragraph.
There are lots of visual effects libraries based on jQuery as well (as plugins), some are quite mature.
I personally find jQuery's approach better suited for DOM scripting, but your mileage may vary. I would encourage you to run through an intro to both and see if one grabs you. You may also be interested to know that jQuery allows you to modify the name of the $() function so you can use prototype as well... maybe you'll end up choosing both!
Good documentation is key:
for prototype:
http://snook.ca/archives/javascript/pro ... heatsheet/
for jQuery:
http://www.visualjquery.com/1.1.1.html