I own an M140 and have driven a couple of fast minis including the GP. Without a doubt the mini will be more fun, with a manual gearbox it would be even better.
My 140 is an auto and it is stupidly fast but feels less fun than many of my previous hot hatches. It is more practical and dare I say, less girly than any Mini.
As a second car purely for fun I'd be inclined to pick a Mini, but not an auto or a convertible.