In my Give me Deus Ex, Foxiest, and Pacifist run through, I chose the stun gun.
Suffice to say, it was useful for like only two parts in the game- the first mission and for the Good Soul achievement, but it was fairly useless afterwards.
It's only real useful when you, for example, fight two guys and only have enough energy to take down one, so you stun gun the other.
I found the Tranq gun much more useful as it hits guys from a far plus it has a silencer. Besides, if you get close enough to stun someone, you might as well use a takedown anyways. --- For to win one hundred victories in one hundred battles is not the acme of skill. To subdue the enemy without fighting is the acme of skill. ~Sun Tzu
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. --- http://azanode.deviantart.com/