Shooting any AR pistol without hearing protection isn't a good measure of loudness. Caliber, barrel length, and type of muzzle device all affect it.
Addressing the velocity, running a .300BO at 8" is about the same as 5.56 at 10.5". It's still apples and oranges, what we are really measuring is the expansion room of the powder inside the barrel, how much surface area at the base of the bullet is exposed to absorb kinetic energy, and the amount of time it's exposed to that pressure before exiting. As a rough measure, the larger the bore the shorter the barrel to make the same power levels. That is just a rough guideline but why you see 5.56 recommended no shorter than 10.5 but 6.8 and .300 as short as 8 to make the same kind of number.
That is more a dynamic concept of operation, as many posters could show all sorts of numbers arguing the opposite. But it's what the gun designers are coming up with and the packages they sell in volume. The first one was the XM177 in 1965, so this has been going on for over 50 years now.
How much a velocity drop? Much less than some think. A 5.56 from a 20" barrel is typically said to run 3300 fps. We don't see that now, as the M4 runs a 14.5" barrel, and our lookalikes at 16" are comparably close. 2900 fps is normal for a 55 gr round. Move to a 10.5" tho, it drops to 2700 - not that big a bite, with the 70 grain OTM running over 2500. That draws in the 1000 foot pounds of force to a shorter distance, about 80 meters.
Looking at handgun specs, the designers of the guns for the Army Pistol trials of 1954 specified 400 foot pounds of force were needed for handguns, which typically only have a 50 foot effective range - about 17 meters. The gain in effective range and power of a rifle caliber pistol is simply huge in comparison, which is why we do it. Add having 50% more ammo, too.
For that, we carry something quite a bit bigger and much harder to CCW, if ever. So, no, there isn't that big a velocity loss, and second, you make up for it by making the bullet heavier, bigger in diameter, or lengthening the barrel.
At this point it's all good right? Nope. We haven't discussed ammo costs. And that is where it starts to hurt, as there is NO cheap surplus 6.8 or .300. There is some cheap import stuff, but not a milspec NATO power level combat round for use in self defense or hunting. If you want to practice for cheap then the commercial rounds invented to upgrade the power levels aren't going to be and you will pay extra for the ammo. As much as 2.5 X the price. And that affects training. Those on an unlimited budget who get to blow away ammo all day long 5 days a week don't care, but the other 99% of us have to consider it.
That is why after I had already built a 6.8 AR for deer hunting, I choose to build a 10.5" pistol in 5.56. I don't shoot that rifle much. It's nice, my son likes it deer hunting, but it's not my first choice in the field. That pistol in 5.56 is - because it's a pound lighter, and because I can shoot it at the range for half price, which means twice as much per $20 for ammo. If I can shoot twice as much for the money spent, then that is a big factor.
The deer won't be able to tell the difference, mapping the hunting area I've worked over for 40 years, all the shots were under 80m anyway. 1,000 foot pounds of force is ethical and effective, it's shot placement that counts. and practicing twice as much with a 5.56 pistol means I'm at least as good as with a rifle and red dot. Less effort in the field, too with a lighter shorter gun.
You could do the same with an 8" .300BO supersonic but the ammo costs are the difference. It's going to be more expensive round for round. There is no cheap surplus.