Standard load of two full pouches and a full magazine in the rifle:
M-14 - 2 x 20-round mags per pouch and 1 in the piece = 100 rounds
M-16 - 3 x 30-round mags per pouch and 1 in the piece = 210 rounds
The lighter 5.56mm round was adopted for "spray and pray" jungle warfare where the ranges of the firefights was expected to be very close and volume of fire was more important than maximum range.
Also, a loaded M-14 weighs over 12 pounds, an M-16 about 7 1/2.
Actually (according to the US Army), the current M-16 runs 8.8 pounds, including a sling and a loaded 30-rd magazine. And while the M-16 has been putting on the pounds over the years, the FAL has been dropping them. My favorite FAL (and it's one I built myself, not an exotic toy ;>) weighs in at about 10 pounds even (including the sling & a loaded 20-rd mag).
For a difference of about 19 ounces, I would personally take the 7.62 FAL over the 5.56 M-16 any day (but that's just my opinion)...