Hi posted a SV650 swap, now I'm unsure about the high being a bit of an issue for changing the ride and feel of the bike. I don't necessarily want that. I keep leaning to the R6, best choice probably?
The R6 doesn't raise or lower the bike at all so perhaps that'd be a plus for you!
What's your weight (with gear) ?
The R6 shock provides the most adjustability... but heavier riders seem to prefer the Katana shock (so I've read).
Those who've tried them all seem to like the R6 shock the best. I have a Katana 600 shock and I like it just fine but I am a "heavier" rider for sure. It did raise the ride height a little, maybe 2cm.
I have only installed the R6 recently and being only 65kg and not setting it up yet and the spring being on the lightest setting, I found no difference in the handling. But a noticeable difference going over bumps and a much better experience even with another 65 kg passenger and the suspension still felt good and I could certainly bump up the settings. So while having no experience of the Katana shock it seems to me that the R6 would not be bad for a heavy rider.