IF there is a difference in armor penetration between old .30-06 and newer NATO 7.62 rounds, it is NOT a velocity issue.
It is a bullet design and construction issue.
The were a number of primary reasons why the military wanted to shorten the .30-06 into the 7.62:
1. Reduce the raw material burden. About 1/2 of an inch of the .30-06 was air space, and it was unnecessary. During World War II there had been critical shortages of copper, which translated to ammunition shortages.
That small amount of brass savings might not seem like much, but when you multiply it by 10-12 billion (a rough estimate for how many rounds of .30-06 were produced yearly during the war years), it adds up...
2. A lighter cartridge means a soldier can carry more. Not as dramatic a difference when you look at the difference between 7.62 and 5.56, but it's there.
3. The powders in use at the time burned more efficiently and uniformly when they were slightly compressed. The same is true today with IMR-4895.
4. A shorter receiver is a stiffer receiver, meaning overall better accuracy potential.
As for the M-14, no, it wasn't a failed experiment. It was a failed main battle rifle. As a specialists weapon it's been resurrected and is providing fine service.