I don't know what its "suppose to be", it was Dependant on the Units TO&E (Table of Organization and Equipment). As i said that was Suppose to Be but was really dependent on what was going on.
In SE Asia we weren't suppose to go anywhere with out a weapon. If one thought he really needed a weapon, then he would take his issued weapon be it a Rifle or Machine Gun. In the rear or Fire Base, and you were going to chow or to pick up the mail, you grabbed a pistol if you could find one. No one likes to drag a M-60 through the chow line. I had one I carried but few soldiers would carry a pistol to the field, simply because for the weight of the pistol you could carry an extra canteen of water or more ammo. I've never seen anyone carry a pistol as a primary weapon in the field, even officers and medics.
At night you never wanted to fire a '60 from your position unless things really got bad, they looked like a trip flair, so when it was your turn to stand guard you borrowed your position Buddy's '16.
Even senior officers on fire-bases carried '16s, you might see them in the TOC with a pistol but outside they had their rifles and pistols (they weren't carrying ruck's).
When I was in the Guard, my issue or assigned weapon was a rifle but I always carried a pistol because I was too lazy to pack around a rifle on FTXs 'n such. But if I needed a weapon it would be a rifle.
My wife was deployed at the first part of this (Iraq) war. She worked of CFLCC C-2. Her assigned weapon was a M16/203 but she never carried it, she carries the M-9. I don't think she seen the rifle from the time she got there until she left. She was stationed in Camp Doha working for 3rd Army C-2, they would run back and forth between Doha and Baghdad in Rented SUVs (this was in 2003). They weren't suppose to leave Doha without a weapon but weren't required to carry one unless they left base.
I went to Kuwait to stay with her for a while. When she picked my up at the Kuwait Airport I looked around and didn't see her weapon, I asked her about it and she said she had one, pointed out a squirt gun on the dash.
I see a lot more soldiers carrying pistols w/rifles now then I use too, but supply is a bit better now, soldiers now have access to cases of water bottles now, they don't have to carry 5 or so canteens of rice paddy water so weight isn't as critical.
In my 25 years in the regular army and NG, except for reading a TO&E, I don't think I've ever seen written rules or regulations on who carries pistols. Regardless of the TO&E it was based on need or want to, if you were sent to the chopper pad on a mail run, you'd grab a pistol if there was one laying around.
I think right now, If I was playing army, and thought I needed a weapon, I'd take a rifle and leave the pistol in the arms room, if I was just hanging around the rear or peace time soldiering I'd want a pistol.