I'm loving my BV-350, and have (had) only one gripe. The windshield. Now its gone and so is my gripe:
Regarding cornering....I also have a Vespa GTS 250 and don't find my BV any less capable of aggressive cornering than my Vespa...maybe adjust the preload on your rear shocks a notch or two to keep the c-stand off the tarmac? Worth a try.
I've actually come to like the aggressive e-braking...especially in the tight stuff where I prefer riding. I could see NOT liking it in city/stop-and-go traffic but then it IS marketed as a tourer. I wholeheartedly believe the GTS is a better urban commuter, and having never ridden a Sportcity figure its about the same. And since "city" is part of it's name....maybe thats it's sweet spot too.
I rode my GTS yesterday in the hills locally and commented to my wife (also a GT/BV owner and relatively seasoned rider of 10+ years now) that I missed the heartier e-braking of the BV up in the hills of DeLuz.
Enjoy it, it's a different animal but in my estimation one of Piaggio's best product offerings right now.