I'll just do a general address for the main point brought up by VulgarDisplay, Red Hawk and zebrax2.
Having AMD hardware in both the PS4 and the next Xbox should not affect the popularity of PhysX, if precedence is to be an example. PhysX has been multiplatform for a long time, and with the 3.0 SDK release, it's optimized and scales well across multiple CPU cores. So from a software physics standpoint, PhysX will still be a valid choice; particularly considering the powerful developer tools available for PhysX.
As for Hardware Physics, I think it's a moot point. PhysX has always been designed to be scalable. The more processing power you have, the more particle effects can be calculated.
For example, the normal setting for PhysX on Batman Arkham City can run on a single mid range GPU, a long with most of the eye candy features turned on @ 1080p.
On high though, you will likely need a dedicated, or more powerful GPU. So what does this have to do with anything?
The next generation consoles will be able to run PhysX (with advanced particle effects), but on lowered settings. Since they can code a lot closer to the metal on consoles, PhysX on low with some particle effects should run fairly well on the CPU cores.
Devs will tailor the amount of particle effects based on the available resources (which depends on several factors), so as not to overburden the CPU..