It depends on the difference in the bike. My current bik is a 6+ year old hardtail with aobut 1-2 inches of front travel, my next step up will be huge. I am constantly held back by my bike because of its crappiness.
My dad rides a fully suspended bike with good v-brakes etc.., he will be stepping up to something like a fuel 80 with hydraulic disks, deore xt etc... His step up will not affect his riding that much.
The rider:bike ratio ranges depending on the bike!