Better choice of modern rubber with the 17" rear, an alternative choice in multi-compound would be a 160/60 18" Bridgstone BT016? No BT016's avaliable in an 18" 150/60...The 17" rear would (marginally) drop the back end - slowing the steering, but this could be resolved by a longer CBR600 rear shock )

** The NSR250 MC21 rear wheel fits the disc and sprocket carrier from the NC23

Graeme France (GF) may be able to help you out with one on here....

Metzler provide a tyre for the standard 18" NC23 rear wheel. I'm switching to one today after removing a Bridgestone. I'll let new visitors know how I get on with it after a good running in.

Very little effect really unless you ride like Rossi.
The advantage of the 29 rear wheel is it's a 17" rather than 18" and gives you a greater choice of tyres and makes as its more common.
That's it really"!
H rated tyres like the 090 are fine.
I have super sticky zr rated tyres for track but its so much easier just to run 090's and not have to mess around changing to wets if it rains