Earlier quoted context omitted.
Thanks for the perspective. I have never experienced either directly so at best I'm speculating although I've been around many people who have been through both. My basis for making that comment is that at least ostensibly you get due process in the legal system. Hope you came out the other side in a good place.
Involuntary commitment from mental health is a min. 72 hours here, but I think you can be in and out of a drunk tank faster than that, which is usually just a few hours to sober up. I could see a bail hearing happening quick enough that you get in and out before 72 hours, but I don't know how common that is.
[0] That's how long it took for me to get a court date at which point I was released with time served (2 weeks). Getting out of the mental hospital never even required a lawyer (though I'd still recommend retaining one if you're ever in this situation).