You know I looked at the published weights of the M14, 8.2 pounds unloaded, and that is not that much different from a M16A2 at 7.8 pounds.
The weight of a 308 version can be more or less than a M14, depending on how much metal the designer puts on the thing.
I have extensive experience with the AR15 platform and the M1a. I have shot a couple of Ar10's, was very surprised by the relatively low level of recoil.
I am of the opinion that if your one and only criteria is accuracy, the AR style of mechanism is going to be more accurate. The bolt lugs evenly distribute the load. The M14 lugs are asymetric and the loading is asymetric.
But accuracy is not the whole thing.
Clearing a jam in a M14 is easy. Though I can't think of every having a jam in a M14/M1a. I remember once kicking the operation rod open for a newbie. His load was way too hot.
Clearing a jam in an AR is more difficult. I love the open top design of the M14, just look down and see what is going on. Any issues with stacking, jamming, you just reach in with your fingers and clear it. Most AR service rifle highpower shooters carry a multitool. Something with needle nosed pliers to reach in that ejection port and pull out a case.
Just this weekend I separated the halves of an AR, because it is easier that way to clear the upper, and rammed a cleaning rod down the barrel to clear a cartridge. I could not grasp the rim with enough force, with my Leatherman, to get the thing out. It was too deep in there to use the screwdriver blade.
I find clearing blown primers a lot easier in the M1a. Just pull the trigger group and the primer falls out. Separate the halves of a AR, fish around with your multitool, beat lower against ground hoping that will knock it loose, maybe the primer will come out. For deep cleaning you have to push the pins out and remove the trigger parts.
Cleaning the locking lug recesses in an AR weapon requires about 15 Q-Tips. Much easier on the M1a.
I think the M14 was a better design. Even if the weights are equal.