I think the question is: which bike has been sitting on the dealership floor longest?
Though I haven't ridden a SV650F, I have ridden the naked variant, the more popular SV650. It's a great bike: the transmission is butter smooth and gives great feedback, the clutch was super easy to modulate.
What did it for me on the FZ6R was the sound of an inline-4 at WOT with a pipe, plus the suspension seems a lot more buttoned down, out of the box.
Talk about instability is rubbish. I did feel a bit more buffeting before the accessory double bubble windscreen, but that's about it. Look at it this way; if it were an issue, there would be post upon post about it (such as the CBR1000RR engine oil issue), and if the issue was particularly bad, I'd expect a recall, or some sort of stop sale until the issue was fixed.
As others have said, feedback here will be undoubtedly biased, but if I were doing it again, I'd probably end up w/ the same bike.