Considering that if your round doesn't stop him you might very well die, i can understand wanting over-kill for use on big cats.
I would definitely err on the side of too large in that case.
A highly reliable .45 ACP with night sights and loaded with good, sturdily constructed 200gr JSP +P ammunition (i doubt they're commercially available so you'd probably have to hand load them) would probably be my first choice for 4 legged Cougars (For 2 legged cougars i have other "weaponry" that i employ.
).
Fortunately there are no mountain lions in Philly. All our predators here are of the 2 legged variety.