I read that the M-14 was virtually uncontrollable in full auto, resulting in deactivation of F/A.  Yet the BAR earned quite a reputation in battle.

Given a comparison between the 7.62X51 and 30.06 cartridges, why the difference in controlability between the two rifles?

Didnt the BAR weigh 20+ pounds, and the M14 was only 9 pounds? The extra weight probably had a LOT to do with it.
Plus the BAR was used as a machine gun, the M14 was intended as a rifleman's weapon. IIRC, they left a couple of M14's per unit with FA capability, to serve that SAW role.

BAR: 47 inches long, 18 lbs (appx) loaded
M14: 44 inches long, 11 lbs-loaded.  

The BAR weighed about 20lbs or so.  The stock (from memory) is more of a straight line also.

M14


BAR

You just have to hold and shoot one to know why.

As noted the BAR weighed a great deal more.  The barrel was much heavier, and the cyclic rate was much lower as well.  On the 1918A2 (which had selectable rates and no semi) the slow rate was around 350 rpm and the high rate was around 650 rpm.  The M14 weighs some 9-10lbs less, has a standard rifle weight barrel, and the cyclic rate is up around 750+ rpm.  

The M15 was originally planned to replace the BAR.  It was an M14 with a heavy barrel.  It was dropped from production when it was decided that the M14 would do double duty.  Hence the jump from M14 to M16 in the rifle numbering sequence.  Later the Army had to develop the M14A1 to do what the M15 would have done in the first place.    Well, it's not like that's the only time the Army reinvented the wheel

Ross