The advantage of running it twice is that it reduces variance (negative and positive) in the short term. In the long term, results should smooth out, and it should make no difference. Running it twice does not change your EV at all.
It can be beneficial if suck-outs put you on tilt. For example, you get it in with a set versus a player with a gut shot. Your opponent hits his 4 outter on the river and wins the pot. That suck-out might put some players on tilt for the rest of the session. If you run it twice, chances are the 2nd run won't complete your opponent's gut shot, and you'll chop the pot. Less tilt.
It can be annoying in spots where you get it in good, you win the first run, but your opponent hits his 4 outter on the second run, and you chop the pot. Notice this is exactly the same as the first example, except in the opposite order. Mathematically, each is exactly as likely to happen.
A second run only happens when both players get it in and have the option enabled. And of course, fish almost never have run it twice enabled, so usually it doesn't even matter.