The PS3 doesn't have backwards compatibility with the PS2 anymore, and only has software-based backwards compatibility with the PSX. If there's some big differences in the architecture for the PS4 then there'd be no way to do software-based compatibility that would run on any decent level. The 360 also only has partial backwards compatibility through software, and things claimed to be compatible vary greatly in how well they run. There's a good chance the xbox's next iteration also won't have backwards compatibility.
The http://4.bp.blogspot.com/-XukjbgZHePY/ThrwdtnllnI/AAAAAAAAAFc/84iPKsnisag/s1600/PS3s.jpg of the PS3 still has backwards compatibility with PS2...
PS3 controllers didn't even have Dualshock support until 2008. Comparing my old controller with my new one, the Sixaxis-only one feels as light as a feather.