Chrome has libxslt; FireFox has something called "Transformiix". Both 1.0. Chrome has no extensions, only 'exsl:node-set'; FireFox has quite a few, although not all of EXSLT.

Plug: here is a small project to get the basic information about the XSLT processor and available extensions. To use with a browser find the 'out/detect.xslt' file there and drag it into the browser. Works with Chrome and Firefox; didn't work with Safari, but I only have an old Windows version of it.

https://github.com/MikhailEdoshin/xslt-detect-ext/