Part of the idea is to make it easy to add functional utility methods to an existing project without making any other assumptions. You can use it with whatever OO scheme you've got cooked up, any Ajax library, and any DOM-manipulation framework.
I have found Prototype much better for a "web-app" framework - I can build up complex controls and effects with the "OOP"/Inheritance framework, and I have access to all the functional tools I'm used to from Ruby.
JQuery, on the other hand, has always felt "lighter" - really great for a quick Carousel control on a marketing site, or a pop-up effect or something like that, but it quickly turns into spaghetti with anything more complex.
I'd be interested in other people's views on this split, especially people with experience using a whole toolset like yourself.