http://caniuse.com/#search=history will give you an indication of what supports the current version of pjax.
The severside code that sniffs the request for PJAX header could also react to the browser and degrade nicely for other browsers.
http://forum.kohanaframework.org/discussion/8869/kopjax-simplistic-pjax-jquery-ajax-module/p1#Comment_60090 is a decent list of alternate options.
If you don’t mind missing support for other browsers or make changes to do so then PJAX’s only draw back I can see is the need to have 1 chunk/partial to update.