I have an FZS1000 and my daughter has an FZ-07 (same as the MT-07, just the US denomination), which I ride occasionally.You need to try the FZ-07. The engine has a lot of torque starting really low and it may surprise you coming from the Fazer 600. It is well balanced and you do not feel any vibrations to speak of.
However, it's a twin, so it's not as smooth as the I4, and being completely naked, it will be a change from the Fazer if you do any medium or long distance rides. Around town, it's a hoot.
I have not ridden the FZ-09 (or MT-09), so I can't comment on that.