One of my big things is home sharing and streaming between devices. You can do that on the PS3, but it's not reliable or intuitive.
If you mean streaming music/videos off a PC, the 360 can do that as well (you have to enable the service in Media Player/Zune). That same step is required for either PS3 or 360 to see the PC's media library (called DNAS on the PS3 if I recall).
I've had that working for some time for both my Ps3 and 360. My D-Link 321 NAS has it built-in, so it just worked.
I assume it'll work on PS4/Xbone as well.