This isn't about a side-by-side technical comparison, rather about how to "think in jQuery" versus "thinking in Prototype".
I've used Prototype heavily for several years, and jQuery somewhat less heavily until about a year ago when I started doing a lot with it.
With Prototype, I can write some fairly elegant code; my boss once reviewed a large amount of my code and remarked that it was the first Javascript he'd ever found a pleasure to read. I understand - and understood pretty much from the beginning - almost instinctively what Prototype's trying to do, and know how to work with it.
My jQuery code is a lot more, how can I put this, "workmanlike". I feel as if I'm fighting jQuery every step of the way. I have to (try to) force myself to stick with it and not drop down into "native" JS, where I know I could bash out clean cross-browser code more quickly. Working with it more makes it more, not less, frustrating.
It's not (or at least not entirely) a lack of familiarity with the functions available. I'll often know I need to use a given function, but the way in which it's used seems truly bizarre. That's usually a sign that I'm coming at something entirely the wrong way.
The more I think about this, the more I think I'm trying to use jQuery in a Prototype way.
There has to be some blinding flash of light that hasn't happened to me yet. Especially if you've worked a lot with both, what do you find are the most fundamental differences in approach? How do you need to adjust your mindset when switching from one to the other?
Don't be afraid to state the blindingly obvious, because it may just be that blinding flash...
The best advice i can give is "Embrace this". In jQ, you're nearly always talking about iterating over a set that is wrapped in the jQuery object. Invoking one of the set's methods performs the method on all the elements of the set, whether its 1 or 100. That method is always going to return the same instance of the set (aside from accessors that get a property). In the context of the interation this is the value of the item in that set youre manipulating - usually the raw DOM Element, but it could be the value of an object property or array item.