I have a new to me 2007 FZ6 and my good friend and normal riding partner has a 06 SV650. I actually rode both this past sunday, we did a bike swap about half way thru the ride.
The SV is a quick "little" bike. I mean that it feels smaller, handles smaller, and isn't as stout on the road. I feel much more stable behind the bars of the FZ. The rear tire is a 160, and the FZ has a 180 if that means anything to you. The suspensions are both equally not adjustable. So they'll both likely need some tinkering with the suspension to suit your riding down the road. The power curve of the sv is a lot lower, but above 5k the FZ will leave it behind. Trust me, I know. We did some roll on's on both bikes, and then swapped bikes and did them again. It wasn't a huge difference, but from 50-100 in 4th 5th and 6th gears the FZ would pull away from the SV once wound up. The FZ has a smoother transmission shift than the SV as well, the "snick snick" feeling is a bit more pronounced and I personally thought it was more confident in the shift. The parts are ABUNDANT for the SV, huge aftermarket support. Lots of options for exhaust, levers, etc if thats your thing as well.
All in all, he even admitted the FZ had an edge over the SV. He said that if given the choice of the two, he would have likely chosen the FZ instead!
Hope that helps!