But cats run out of puff much sooner -- so it will depend upon the distance -- a bear would always catch a puma if it could keep it in sight, but a puma would also always catch a bear, sooner.
Humans can outrun almost any other animal -- eventually. Horse-versus-runner races have to be set over just the right distance (I think about 30 miles) to make them fair -- too little and the horse always wins, too much and the runner always does. Women overtake men if the trip is long enough, too...