According to PlayStation 4 documentation provided to Digital Foundry, Sony's next-gen console reserves 3.5GB of its memory for the operating system. This leaves a total of 4.5GB for developers to work with.
In addition, the outlet goes on to note that apparently 1GB of "flexible memory" may be pulled from the 3.5GB dedicated to the OS in certain circumstances. As such, developers could potentially have up to 5.5GB of memory to work with, with 4.5GB being the absolute baseline.
This puts the PS4 on the same general level as the Xbox One, which requires 3GB of RAM for its OS. So, Xbox technically has a larger amount of baseline memory available for developers (5GB vs. 4.5GB) but taking into account the 1GB of "flexible memory" the PS4 has going for it, I'd say it probably will end up being a wash.