Since everything gets compiled down to Javascript in the end (and Objective-J doesn't feature 100% browser compat either) I don't see how they can offer anything not possible with Javascript to begin with. Actually that's a question? I don't understand how it is different than, for example, CoffeeScript - but I would be happy if you could explain how it is.
You also shouldn't confuse the language (Objective-J) with the Cappuccino framework. Objective-J is just about providing certain language level features on top of JavaScript, the same way Objective-C implements features on top of C. It's also 100% cross browser, so I'm not sure what you mean by that.
Cappuccino is a full fledged framework for building apps which run in a browser. I'd argue that it's the best, but my opinion would hardly be unbiased. It does in fact implement an API for using Canvas (which also works in IE). Though, that isn't a JavaScript feature. And pretty much nothing in HTML5 is present in 50% of the browsers out there.
But if you don't like a particular part of the abstraction layer provided by Objective-J/Cappuccino, you're definitely free to use raw JavaScript. Just like in Objective-C you're free to use structs, function pointers, and C-style arrays.
Nobody even noticed.