Well, the question is not well constructed. It's a bit like asking whether asparagus or avocados are a better vegetable.
Did they take advantage of the near-decade of experience gained between one and the other, certainly. They wanted a lot of "commonality" for those "used to" a pistol who were to be moved to the Carbine. Which was menat to be artillery, admin, bakers, cooks, truck drivers and messengers. (Officers and NCOs were not meant to be given new arms, that was War Department meddling later in the war--a lot of things not "meant" to happen did; was only supposed to be one BAR per Rifle Squad, yet some had as many as three.)
However the Army wanted it to use the billions of rounds of .30 M1 ball ammo. We can thank Dugout Doug for that one. The 276 Pedersen rifle was the clear winner in the trials.
This is tricky going. The 7x53 had a lot to recommend it as an infantry round, weight, LOA, etc. What it was not (and had never intended to be, was a Machine Gun round. US MGs were, in the mid 30s still intended as base-of-fire weapons designed to interdict the enemy from ranges o 900m to 2500m (and operate over the heads of US troops in the in-between). That was going to require M2 ball (or related specialty ammo). And the War Department had plenty. Congress, in the mid 30s was more concerned about keeping themselves rich than spending any more money on an Army that was never going to be needed again (pay no attention to the dictators in both the East and West). So, Congres was likely going to force the War Department into only one caliber. And Armored Corps was really committed to cal..30 MGs in their new tanks that wanted to build thousands of.
Then, there's the "range fan" issue. War Department had managed to get CCC and National Recovery Act commitments to build new rifle ranges for a bunch of Army Camps. Those ranges were based on M2 ball. The 7x53 had a higher arc from the BC and lighter weight of the projectile. That meant the range fan safety zones wer about a third under-sized for the new round.
So there's a pretty big gap to get the 276 across, for acceptance.
If the Army and DD had not stuck their noses in it the Garand would have been a totally different rifle. In fact I doubt the M-14 would have ever been built.
Well, yes--no "bend" needed in the op rod, for one (it's needed to clear the larger chamber bulge). Getting a smaller, lighter Garand would have been much easier, too. A box magazine would have been easier to gin up. Or using a shorter gas system, and/or a shorter barrel. Peterson's first submitted rifle was a toggle-lock, basically a lever-delayed blowback--so the Garand could have been lightened considerably.
The other interesting part about such speculation is in that the BAR might have been looked at again, with perhaps a pistol grip, almost certainly better magazines, and with charger loading (remember that most of the M2 ball is on 5 round chargers in bandoliers in 1933).