Web Browser support Windows Embedded vs Windows CE vs Windows Mobile?

I am developing a web based inventory solution for a client and there will be handheld mobile computers involved. I've never developed a web app that has been run on a browser on one of these devices. The devices we are looking at have one of the following OS:

1. Windows Embedded 6.5
2. Windows CE 5.0 or 6.0
3. Windows Mobile

My questions are:

1. Do all of these come with some version of Internet Explorer
2. If so, does that version of IE support things like: javascript? JQuery (UI, AJAX calls)

Any experience or recommendations on any of these OS choices, pros, cons?

No, they do not have the same version of IE. All of them support a subset of javascript, but what they support differs between them and I'm not aware of any document that lists what is (or more importantly, what isn't) supported.

There are some subjective lists, for example [jQueryMobile gives WinMo 5.2 a grade of "C"1. Basically it's a story of "don't assume anything will be there. Test, test, test."