I've definitely never had any sort of constipations on benzo's, even when I was taking 12mg Xanax a day. I don't think benzo's cause constipation. I've never heard of that.
I actually have never had constipation from opioids either, not even on very high doses, In fact, for some reason codeine (only codeine) gives me extreme histaminergic reactions: I took 300mg once (no tolerance at the time, though). All of my skin turned red and I was bleeding all over from clawing at my skin. Never felt itchiness like it it was like torture. My face swelled up, especially around my eyes, My blood pressure was so low I was stuck lying on the floor (couldn't sit up or even lift my head; had to shout to my parents for an ambulance). Sorry, went off-topic a bit there, but the interesting symptom I got along with the others I mentioned: I got very severe diarrhoea. Like, bowel cramping and copious amounts of watery diarrhoea every 5-10 minutes.
So yeah, I'm weird. Codeine gives me the shits big time.