Bill Phillips
Most people use energy as a first approximation, with bullet
design just as important but harder to assess.

Bullet behaviour on impact is of decissive importance
when assessing the effectivity ("stopping power"). FMJ
7.62x39 tends to be relatively stable on impact in soft
tissue, it just turns 180 degrees to leave base first, but
does not break up nor tumble more. Thus the 7.62x39 bullet
often tends to go through the target relatively cleanly,
expending only a fraction of its energy in causing damage.

Lighter, smaller calibre, but faster, assault rifle rounds,
like 5.56x45 and 5.45x39.5, are much less stable on impact.
The higher speed and smaller diameter to lenght ratio, tends
to cause lots of tumbling in soft tissue. 5.56x45 also tends
to break up, while 5.45 with its bimetal design tends to deform.
The higher speed gives a stronger shock wave too. Thus a larger
percentage of the energy of these rounds is expanded inside the
target, causing more severe wounds at normal battlefield ranges
(at long ranges, however, the target effects are much reduced).
5.56x45 is actually _more_ effective against soft tissue at
typical ranges than slower full-sized FMJ rounds, like 7.62x51,
which tend to go through the target with much of their kinetic
energy still left. (Rifling is most relevant here too, eg 5.56
at 1:7 is more stable and less lethal on impact, than the former
standard, 1:9).

5.56 is also intrinsically better at armour penetration than
7.62x39, as the surface pressure is larger due to the smaller
calibre. Otoh, armour-piercing capability depends a lot on the
bullet design, and I dunno how the various dedicated AP bullets
compare. Full-sized rounds (7.62x51 etc) have much more kinetic
energy, and hence allow for more effective AP rounds.

5.56 and 5.45 have lower recoil than 7.62x39, allowing for
quicker/more accurate aimed rapid (semi-auto) fire and better
control of full-automatic bursts. This is a big advantage. The
recoil of 7.62x39 is however low enough for a competent user to
control an assault rifle at auto. In contrast, assault rifles with
full-sized rounds, like 7.62x51, are practically uncontrollable at
full auto. Muzzle brakes can be used to somewhat reduce the recoil,
but at a cost in the signature and/or weight and length of the
weapon.

The lethality of 7.62x39 against soft targets can be much increased
using soft point (expanding) bullets, like hunting bullets, but
these are illegal in military usage. I'd guess that a deforming
legal(?) bullet could also be developed, perhaps along the lines of
the bimetal hollow-tip FMJ 5.45x39.5. Cost would be an issue though.

7.62x39 does have an advantage over the more modern smaller
calibres though. It's less likely to be deflected by foliage,
and is also more effective when shooting through trees or berms
at a target in cover behind. I'd guess that manufacturing issues
were the historic reason why the Germans and Soviets went for 7.6*
in their AR's, rather than a faster smaller calibre round.

Full-sized rifle rounds, like 7.62x51 or 7.62x53R, typically
only have an advantage over modern assault rifle rounds at
ranges longer than normally useful for an assault rifle. The
much heavier ammunition and much larger recoil, make these
calibres badly suited for infantry assault rifles. Hence
all technically advanced armies use lighter intermediate-sized
rounds nowadays. Sniping rifles and GPMG's are another matter,
and there 7.62x51 and 7.62x53R still prevail. The particular
terrain (typical lenght of LOS) is also an issue here.

Otoh, short-barreled small-calibre carbines, like M4, have a
reduces muzzle velocity as compared to normal lenght AR's, like
the common M-16. The lower muzzle velocity of M4 impairs lethality
beyond 100m or so, which is already relevant.

Another issue is bullet drop. The faster the bullet, the less
there is bullet drop. The relatively slow 7.62x39 does particularily
badly here.the bullet drop of AKM (7.62x39) is about 70cm, which makes
adjusting the sights or aim necessary at the longer normal infantry
ranges (ie up to 300m or so). 5.56 is also superior in this respect
to the 7.62x51 at typical ranges.