I wanted two scoots in my garage, it would be the Kymco GTI300, and the Piaggio BV 350.
500cc and up scoots are too heavy. Most 500 run 500+ pounds Usually, 550 pounds or more. Over 100-150 pounds more than the 350.
If you look at the specs on the 350 and 500, (power to weight ratio is close.)
So performance should be good on the 350 without the extra weight.
My problem is the only Piaggio dealer in my area closed their doors two years ago.
The 500 has more vibes but, more power goes with it. On the flip side the 500 will give a little smoother ride because of its weight.
The Piaggio 500 is a very popular scoot.
There are times I would consider the 500 but, no dealers in my area.
I suspect, in the performance category, there is probably not a lot of difference between the 350 and the 500. Power to weight ratio.