Grain refers not just to bullet size but powder as well. A higher bullet weight gets less powder (to maintain safety in firing). This is because the heavier bullet has more friction and cannot be fired at the same speed as a lighter one without risk to the barrel. That being said, the difference in different grain ammunition of the same caliber is very insignificant when you're talking only about the impact to a target at relatively close range. You can put it on paper, but it's not going to be very detectable in the real world.
Small caliber, high speed rounds lose a lot of energy over distance because the resistance from the air slows them more than larger bullets. The M16, with greater muzzle velocity, has shorter effective range than the M14... which is basically a .30 cal round. The military concluded most fire fights were 300 yards or less, so the shorter range of the M16 would be adequate. And as the round is smaller and lighter, soldiers could carry more rounds on their person. As far as "impact" goes, more than one meaning.
Lots of good points made by all, particularly Redneck. There have been reports of 5.56 rounds passing cleanly through bodies without any damage at close range. The round's devasting terminal effects come from it yawing or tumbling in the body. As a military round, it is FMJ, so there is no mushrooming like you get with a HP. If it manages to pass through without yawing, fragmenting or tumbling, it leaves a pretty small hole. I think that is a very rare occurrence however, and the most likely result of a close quarters hit is a big wound cavity. Velocity is not the end all and be all of performance. Otherwise, the FBI would not have standards that involve expansion and penetration of ballistic gel after passing through clothing. One of the knocks on the Liberty round apparently is that it is so light, it doesn't get much penetration in ballistic gel. It certainly tore a giant hole in the clay in that video though, and that was after passing through Class IIIa body armor.
Run the math on a 162gr 7.62x51 against a 62gr 5.56X45. v is squared but the muzzle energy is more than double. Standard NATO ammo for each.
Well, of course... you're comparing a bullet nearly 3X the mass of the other. Your comment is off point, but I can see where I wasn't as clear as I could have been in mentioning "mass vs. velocity".
I am making your point that the 7.62 has only twice the MV yet at 3x the mass. MY point is that we are limited to factory bullets even if we are reloading. Obviously there must be some utility in the 160 grain commercial bullets. We are limited to what is commercially available. If velocity is all that matters then we would be shooting ARs chambered in .220 Swift. The fact remains that 7.62 possesses three times the MV. The utility in 5.56 is largely in firepower (capacity). I do not believe that 7.62 has twice the stopping power--but I would much rather carry 500 rounds of 7.62 then say 800 rds of 5.56.
Kinetic energy directly related to stopping-power. Yes, you can carry more 5.56 mags than 7.62. Can you carry three times more? No. I know the relationship is not linear, but there are no advantages to 5.56 over 7.62, other than recoil.
Also, 7.62 gains in efficiency by comparison when discussing loaded weight--bullet, cartridge and powder mass. While larger; 7.62 mags are only marginally larger.
If you're in a situation where all the ammo you have is what you can carry, I suspect you would prefer to have 800 rounds of second best over 500 rounds of best. When you're out, you're out.
Anyway, this is mainly academic. The OP was concerned about home defense. No one is advising using .308 inside his house.