Back in the late 40s and early 50s they did testing with .50s and 20mm guns and found the .50s performed better at altitude. Unfortunately the reason they were testing was to arm the B-36 Peacemaker, which ended up with the inferior 20mm guns. I just finished a great book on the subject. I'll try and dredge it up.
Performance of the machine gun or the terminal performance of the projectile?
Between the two, the terminal performance of a 20mm projectile, filled with HE is vastly superior to the terminal performance of a solid .50 cal slug (or an incendiary).
Until the advent of the M39 and later the M61, the US had trouble getting a reliable 20mm cannon. We never could get the Hispano-Suiza design to work reliably enough for our liking, not that we didn't try... the M1 20mm, the M2 20mm, the T31 20mm, the M3 20mm, the M24 20mm and the Navy's Mk 12.
From 1952 inwards (the year the M39 was introduced into service), the .50 caliber was never seen on new designs (the B-52 was the last design to use the venerable AN/M3 .50 cal. Part of the reason the .50 cal was still viable on the B-52 was the fire control radar, which tracked the bullet path and the target path, and given that if the target was in the firing cone behind the B-52, he was committed to thew tail chase and not likely to be able to maneuver enough to avoid being hit, or unaware of just how far back a .50 cal could reach. They could reach back almost as far as some heavier Soviet cannon could reach forward. Namely, because a .50 cal slug with half its muzzle velocity (about a mile back) hitting an aircraft going 600 mph is the same as a .50 caliber slug hitting a stationary target at 600 yards/
Neither the B-36 and the B-47, had the fire control nor the speed to make .50 caliber machine guns viable as defensive armament. Especially when you consider the Soviets were arming MiG-15s with a 37mm cannon in addition to two 23mm cannon.