The bolded isn't quite true. The vita is only bigger than the 3ds only if you count certain dimensions only. The original 3ds is basically a small square whereas the Vita is a large rectangle. The Vita was wider, sure, but it was also more comfortable to hold and smaller overall.
No the VIta is bigger, period.
3DS is 13,4*2,1*7,4= 208 cubic centimeters
Vita is 8,5*18,3*1,5= ~272 cubic centimeters