I can't speak for the Gen1 or 2 but my Gen3 feels every bit as nimble compared to my ZX10. I also went with a slightly taller (200/55) rear tire which makes it steer even quicker. For me the big difference between a liter class sport bike like my ZX10 and the busa are brakes and suspension. As far as turn in and lean angle the busa should be plenty nimble. Check out your setup as others have commented, tires, sag lots of people like to lower and stretch busa 's which can make it feel like you describe.
I havn't ridden a Gen3 yet, but you say the same as alot members here, about how well it handles.
It's also said that it handles much better and feels lighter than a Gen1 or Gen2 from members who had/have both, and I belive it.
I have ridden many Gen1's and Gen2's, and they can be set to handle really well.
Of course they are heavy bikes, and you can definately tell it is night and day from any 1000(which I've also ridden many brands and gens).
I never had any probelm making a Gen 1 or 2 do whatever I wanted it to, nor did I ever have a 1000k walk away in the twisties(we know, alot of variables there), but the weight difference and added wheelbase are very apparent, as the handling feels slower with the weight, but, it also makes the ride feel very forgiving, in terms of a little easier to control over a rough section in the road, vs a 1000, which will dance around much more as they are so much lighter and shorter.
I put 7w oil in my Gen2 forks with stock valving, and it made the forks perform very well with me at 193-195 lbs in gear.
The stock 5w fork oil made the front end feel very flimsy to me, and even though it stuck and tracked good, it felt as if the controls where rubber mounter, a very mushy and muted feel.
The 7w solved that.
And, with all that said,
The Gen1 and Gen2 are some of the Worst bikes to try and ride on a bad suspension setup.
Their weight really shows negatively then, and the front end will steer like it has a 200 tire on it, lol
As much as you travel, you need to stop and try out a Gen1 or Gen2 somewhere, as stock as possible(suspension and brake wise), if I still had one you could take it out and see what you thought of it(but, that offers stands for all of my bikes if you ever pass through Va).
As far as the O.P's bike goes, if the maintenance, chain tension, and suspension are set correct, or resprung/revalved if nesacery, and at stock wheelbase and ride height, we know the Gen1 and Gen2 can handle very well.
It's as if you have to give them a nudge in the direction you want it to go, but it otherwise is as easy to ride as any 1000, and usually smoother on the street.