For the casual fan, I agree wins sounds good, but then I can imagine someone asking: "which games did he win"?
Another thing I like about runs is a wider range of integers. With wins, you have 1, 2, 3, ... wins and there is a big difference between each integer and most of the players are either 0, 1 or 2. Somebody could have 1.5 wins or 2.6 wins, but that doesn't make practical sense. With runs, you have more integers, so you can make a leaders list without decimals.
It's not really a big deal, just a preference I have.