I chose the stun gun for my foxiest/pacifist/hard run if only to stun bosses and make it easier to take out groups without putting points into double take down in the beginning. It was also handy to give someone a quick zap from cover while guards moved around. I didn't have any real problems to be honest. I don't really like sniping and I'm pretty bad at aiming with some of my shots from the tranq rifle not hitting or just alerting the guard in some cases. It was mostly take downs+ the occasional stun. Typhoon and laser rifle for the bosses.
I went with the stun gun. I never felt the need to engage enemies at a distance. If they're that far away then I'm just going to sneak passed them anyway. The stun gun was good for when my battery was recharging or if I wanted to take down more than one enemy.
I don't think it would make much difference anyway, since avoidance and takedowns will form the majority of your approach if you want to be stealthy.