Being someone who owns a 05 FZ6 & an 07 R6S, I'll weigh in on this.
Wider:
ozfazer is probably right about motor mounts being off. The FZ6 feels much wider and Yamaha HxW specs would also indicate so. Most notably, the FZ6 is wider around the gas tank, wider where the gas tank meets the rear subframe, and wider at the rearsets. That being said, it could be just the frame Yamaha chose that creates this wideness. As
kniefi &
I proved on SBN, 03-05 R6, 06-09 R6S plastics will fit the FZ6 with a custom fairing stay and some brackets.
Ram Air:
One thing to consider is that part of what creates more HP on the R6 is that it breathes with Ram Air. I would be concerned of keeping up the intake air flow.
Weight:
As mentioned by many others, the R6 is ~60lbs lighter and it's balance and geometry utilize that to amazing effect. This, above all is a greater differentiator in performance between it and the FZ6.
"Wind up speed":
The characteristics of the performance in 0-35 MPH are roughly the same, with the R6 having a noticeably faster wind up speed. You'll go 0-15 MPH in about the same time, but at that point, you notice the R6 is starting to hit the revs faster, and around 35 MPH, the R6 will build MPH about 30% faster, and revs about the same pace.
ECU:
Also as mentioned by others, the ECU is quite different and more advanced. It monitors many more sensors while responding to inputs more quickly.
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That being said, if you should go through with the motor swap, be ready for a few things. Addressing the narrower and taller R6 airbox and gas tank, addressing ram air intakes, and shimming the engine into the frame. Good luck and I hope you figure it out.