The SOCOM is a nice M14 cut down for a close range rifle. A waste IMHO unless you just like the extra weight. Not a great comparison for accuracy with another rifle.
The SOCOM's accuracy is limited by its sights, the barrel length has nothing to do with it, nor does it really have anything to do with its weight. It basically weighs the same as the standard and Scout/Bush models, and most of the other 7.62x51 caliber military rifles.
If you put a set of Scout sights or a scope or red dot on your SOCOM, your groups at farther ranges will be different than those fired with the CQB sights that come with it. I normally have an Aimpoint on both my SOCOM and AK's, although the targets above were shot using the iron sights on all of them. The only rounds fired from a rest, were the bottom three on the 200 yard target, to confirm zero. All the rest were fired from a cross legged sitting position, with no sling, and at a steady, comfortable cadence.
When it comes to actually shooting any of them and comparing accuracy, I think a big problem is, most of the comparisons are based on target or bench type shooting at bullseye targets at known distances, and not practical field shooting. It amazes me at how many of these super duper target rifles cant hit the broad side of a barn at 50 yards, when you ask the shooter to step away from the bench and shoot quickly standing up.
Peep sights are great for target shooting or more precision shots at longer distances, if you have time. They flat out suck in certain lighting conditions, especially if the light is behind you or your moving in and out from light to dark. Add to this the need to shoot quickly, and it gets worse.
The HK's sights, especially the big open notch, are better suited for all shooting, in any light, 100M and in, and are no slackers for precision shooting out to 400M using the peeps.
Another advantage they have over the M1A is the ability to have tritium sights that are the same size as the standard sight, so you can also have night site capability with no loss of longer range accuracy, such as that suffered by the SOCOM with its big, fat front sight.
Of the three types of sights, (M1A, HK, AK) for anything that required fast shooting, especially closer in on moving, multiple targets, the peep would be my last choice. Over all of them, a good red dot would be my #1.