Mostly, I work on Java EE based projects, and the Java EE has not been updated long time, still version 5.
I don't know whether it needs to be updated.
So how can I benefit from owning a SCJP 6 certification?
There's no strict connection between the JSE version and the JEE version. It's possible to use JEE 5 with JSE 6, in which case you could use the newer features. You're right that the JEE 5 APIs only require JSE 5.
Note that JEE 6 is on the way into the wild, probably later this year. I don't know if it will require JSE 6, though.