I have been shooting Bullseye Pistol for six or seven years. What ammunition I have seen, that I remember, with both the AMU and the Army Reserve is
Atlanta Arms ammunition. The 45 ACP ammunition, I cannot not find on their web site anymore, and I don't know why. But the 45 ACP ammunition the 45 shooters were using is Atlanta Arms 185 gr JHP. I don't remember nor do I really care, about the 9mm ammunition, but it is by the same company.
Maybe you can see the black Atlanta Arms 9mm boxes this AMU shooter is using
Now last year, the Army reserve shooter next to me was using Eley Tenex "Red Box" Pistol Match ammunition in his 22 lr. It was ammunition issued to him. Red box is the most expensive Eley ammunition.
Per my understanding, shooters at the AMU get custom loads while “unit marksman” get regular issue ammo. They just get what seems to work well and horde as much as they can of the same lot number and use it til it’s gone. But I was never military so that is simply what I have heard secondhand and have read here.
When I shot Across the Course at Camp Perry, the M14 shooters were using LC 168 grain SMK loaded ammunition out to 300 yards. I also saw the service teams using Federal Gold Medal match in 308 Win and 223 out to 300 yards. I remember the USMC Rifle Team using Black Hill match all the way out to 600 yards. For years the AMU had their own special 600 yard ammunition, and the USMC had Ammunition technicians loading their own special 600 yard ammunition. But, everything is subject to change. I remember talking to AMU 223 shooters at CMP Talladega, and they had to have loads that ran in everyone's rifle and that was a consideration in choice of bullet, and powder charge. I do believe that price is an important consideration. These teams have budgets. Paying Army personnel to load ammunition is expensive, and if the quality of commercial match is such, that it is not cost effective to have dedicated personnel loading tens of thousands, if not hundreds of thousands of rounds, it makes sense to me to use the commercial ammunition. In my opinion, for a team round, it is hard to beat Federal Gold Medal Match. The stuff has been consistently great rifle ammunition.