I have a 03, which is an older generation than the 06; essentially is the same as Kenny’s 05 minus the inverted fork, and with a 60 front. 06 iirc is the first model year of that generation.
Common consent about the R6 series is it always have a very aggressive riding position, which may feel to aggressive for street riding for some riders. I’ve never ridden other R6 other than my generation and I’ve never ridden a GSX-R 600, so I can’t really comment on them.
I know both bikes have a slipper clutch. I guess depend on price of the two bikes and the amount of mods they have. Try to ascertain what suspension mods thay have (if any) or is the spring rate on the bike is good for your weight (if they are not OEM); Engine mod-wise I would pick the bike with a PC already installed.