The FZS600 stopped production in 2003, and yes the FZ6 is the fuel injected version started in 2004.
But even though they are classed as Fazers they are different bikes, with many very different parts.
I'm sure there are bits and bobs that are exactly the same, but as this is the FZS600 section frequented mainly by people who own FZS600's then in fairness there's no real reason for us to know the answer to that question, unless you've owned both bikes, but even then without literally checking both bars you wouldn't wanna hazard a guess anyway.
Judging by photo's of bar ends per bike on Ebay though, they actually look very different, so i'm gonna guess no, they aren't compatible.