The PS version accepts 4 or more color documents but is processed to 3 color via the built in Adobe RIP. The printer takes over the three color data at this point, which is the same where ever it comes from, driver , raster driver, or other.
There will be slight differences from the raster driver, as it will send a spool file via the driver / system level where as the rip needs only to be sent the data from the application, all relevant containers, links etc. The differences between the PS rip, and the non -PS driver should be very little if any. I am not happy that some HP people are still stuck in the nonsensical mode that for photo printing you need a rip. On top of that the PS version is all but a full feature rip , it's advantages are for accepting more format types, large IP networking, but not at all for better color repro.....