I don't know that one actually handles better than the other, but the larger diameter wheel on the Custom makes it more sensitive to road surface irregularities. The fatter, smaller diameter tire of the Classic is more stable. The Custom tends, I believe, to dive into a curve or turn a bit more abruptly than the Classic, where the Classic is a bit smoother going into a curve or turn--leans and rolls more predictably, IMO. But as for overall handling, both handle very well in my experience. To me, the Custom is best suited for a profiling riding style, although I'm sure it tours just fine. The Classic is much better for long distance riding and touring as it seems to be a bit more "planted" on the road.
"Don't sweat the small stuff---it's all small stuff"
'09 650 VStrom