Both Xbox One and PlayStation 4 sport 8 Giga Bytes of RAM, but Microsoft has been criticized for reserving 3GB for system and background applications, leaving just 5GB for games. It seems that Sony also has similar limitations on PlayStation 4 games' RAM usage.
According to Digital Foundry, Sony's current PS4 developer documentation states that 3.5GB of the console's 8GB RAM are reserved for system and background applications, leaving 4.5GB only to games.
The report noted however that RAM allocation is relatively flexible and that – depending on availability – games might be able to claim an extra 1GB of RAM.
Sources close to Sony revealed that the company's R&D team is looking for ways to optimize the console's operating system, so it is possible that more RAM will be available to games at launch. There are no guarantees for that though.