Seems to me they lost about 100 feet/second and possibly gained some reduction in recoil.
Not exactly correct. They didn't lose ANY velocity switching from the .30-06 to the 7.62mm NATO. NONE!
The specs on GI ammo for both rounds are 10fps apart with 150gr bullet, and there is a 30fps +/- tolerance, so the are, essentially, identical. 150gr @ 2750fps +/-. NO DIFFERENCE!
The difference between .30-06 & .308 Winchester is only in civilian ammo, where the 06 averages 100fps faster than the .308. AND, both rounds, as civilian cartridges are loaded hotter (higher velocity) than the military specs.
The advantage to the 7.62mm Nato for the military was because of the 1/2" shorter case, being a) slightly cheaper and lighter, while still giving the full desired performance, B) the actions are the same 1/2" shorter (and maybe lighter), and C) the shorter case has fewer issues feeding and extracting in full automatic weapons.
When you are talking hundreds of thousands of guns and millions upon millions of rounds of ammo, it adds up to serious money.
We didn't drop the M14 because it was uncontrollable in full auto fire. (yes, the Army did make a big mistake with that, particularly the way they went about it, trying to make the M14 a do it all in one gun)
We dropped the M14 when we did because of US politics in the MacNamara defense dept. Used as a semi auto rifle, the M14 is an excellent rifle, as good as the Garand, and better in some ways. (note, I said rifle, not squad automatic, or SMG, or carbine. For those uses, there are better choices than the M14).
Note that we did not drop the 7.62mm Nato as our machinegun cartridge, even the whiz kids couldn't get us to abandon the proven .30 cal for the .22 like they did for a general issue rifle.