I usually grab my old Ninja 250R instead of the FZ6R for around town, if I'm not hitting the freeway. It's like 340 vs 470 lbs wet. The li'l Ninja is just a lot more fun. Fizzer takes a lot more input effort, and that's with the bike lowered, which I thought helped a bit.
OP, I can kind of summarize the small bikes for you (but bigger than Grom / Z125). I am looking to ditch both my old carb Ninja and the FZ6R for a single small fuel-injected bike.
CBR 250/300 - the least peak power, but possibly the most comfortable and easiest around town.
Ninja 300 - gotta rev it, some complaints about seat comfort. Slipper clutch + abs
R3 - slim bike, no optional abs, new kid on the block w/small community, little aftermarket
Duke/RC390 - torquey thumper, RC is aggressive position
CBR 500 - this 420 lbs bike just never seems to get much love, but comes in 3 flavors (R/X/F)
Ninja 650 - heavy-ish
Duke 690 - thumper but 365 lbs and 64 whp
Street Triple/R - halo 410 lbs 90 whp street bike, but $$$$
Street Twin - very interesting bike, but they made it 480 lbs
FZ-07 - naked twin, 400 lbs, people say pegs are in unfortunate location
BMW has a small 313cc thumper (G310R) on the way (w/usd forks!).
Myself, I would like to try the R3, then N300, then CBR300. Maybe CB500F.
In the USA, there is literally no casual faired sports bike in the middle, around 400 lbs and 50 hp. It's either a 30-35 hp freeway dog, or 460-480 pounds, or $12K+ and 95+ hp.