It's not that a 250 won't go the distance but when I had my 200 I found myself on some hills being tailgated 6' off my back wheel.
Not a comfortable (or safe) situation at all. (Back roads tend to have steeper hills.)
The 350 (after getting an illegal tune-up) eliminated that situation and I didn't have to shift nearly so much.
I felt much safer.
On flat ground it wasn't a problem. Plenty of power there.