When I'm on duty and in the station, or when I'm off duty, I only carry the pager on my person.
When I'm out of the station, on duty (on a call, running errands, cruising the town), I have a portable with me.
My station doesn't issue portables to general members. If I were an officer...I'd be issued a portable and leave it in my vehicle. I don't see any need to carry it 24x7.