The GUI functional automation tools I'm familiar with would all have to have different object map/repository entries for a different browser. This is fairly significant in QTP (w/out robust descriptive programming - but then that is just VBScript, so why use QTP?).
The way that QTP maps web page objects, a truely graphic only change would have little affect. But I think that if the table/cell (location) type move of fields on a page would invalidate the object repository item for that object enought to confuse the 'Smart Identification' - depends on how the change is performed.
A problem is a difference between what is perceived and what is desired, that
we want to reduce (Dewey 1933)
QTP is supporting Firefox. You can have the same QTP script to run with IE and Firefox but the is problem if your Web application is having pop-up. The pop-up object in Firefox is totally different with IE. You have to take this issue into consideration. Refer to the QTP Basic User Guide for details on chapter 28, page 809
QTP supports web application testing a lot better than many open source tools. It's not perfect but there are ways to get around most problems. It performs better in comparison to some of the other leading commercial products too when used for web testing. Just my 2 cents worth.
(I'm hiring Software Development Engineers in Test in Seattle, WA)