Update: I wrote a blog post detailing all the differences much better.
Firefox uses W3C standard Node::textContent, but its behavior differs "slightly" from that of MSHTML's proprietary innerText (copied by Opera as well, some time ago, among dozens of other MSHTML features).
First of all, textContent whitespace representation is different from innerText one. Second, and more importantly, textContent includes all of SCRIPT tag contents, whereas innerText doesn't.
Just to make things more entertaining, Opera - besides implementing standard textContent - decided to also add MSHTML's innerText but changed it to act as textContent - i.e. including SCRIPT contents (in fact, textContent and innerText in Opera seem to produce identical results, probably being just aliased to each other).
textContent is part of Node interface, whereas innerText is part of HTMLElement. This, for example, means that you can "retrieve" textContent but not innerText from text nodes:
var el = document.createElement('p');
var textNode = document.createTextNode('x');
el.textContent; // ""
el.innerText; // ""
textNode.textContent; // "x"
textNode.innerText; // undefined
Finally, Safari 2.x also has buggy innerText implementation. In Safari, innerText functions properly only if an element is
neither hidden (via style.display == "none") nor orphaned from the document. Otherwise, innerText results in an empty string.
I was playing with textContent abstraction (to work around these deficiencies), but it turned out to be rather complex.
You best bet is to first define your exact requirements and follow from there. It is often possible to simply strip tags off of innerHTML of an element, rather than deal with all of the possible textContent/innerText deviations.
Another possibility, of course, is to walk the DOM tree and collect text nodes recursively.