Being a shooter that has fired many 5.56x56 (.223) and 7.62x51 mm (.308) rifles, full and semi-automatic, I must correct you on your assumption that a lighter/faster bullet will travel farther than a slower/heavier bullet. When fired from the same length barrel the 7.62 will travel farther because is HAS more weight. The lighter 5.56 mm bullet will lose speed and trajectory faster than the 7.62 mm bullet. A standard 62 Grain FMJ Boattail bullet (military spec) 5.56 mm will give you a useable 400-500 yards and still have enough kinetic energy to kill a human quickly. A standard 150 Grain FMJ Boattail bullet (military spec) 7.62 mm will give you a useable 600-700 yards and still have enough kinetic energy to kill a human quickly. If you go back to WWII and the 30-06 ( a 13mm longer case than the .308, same bullet) you can get another 100 yards). If the 5.56 were better at long range, Snipers would not prefer the 7.62.
The reason for switching the smaller ( and IMHO inferior) 5.56 mm cartridge is that battles are no longer fought at 500+ yards. Most battles are fought within the 300 yard range. Additionally, the smaller cartridge allows more ammunition capacity in the rifle's magazine and has less weight to allow the soldier to carry more ammunition. It also has less recoil, which is necessary since the U.S. Military started allowing women and small statured men into service.
Don't get me wrong, I love my AR-15 but my M1 Garand (30-06) is just plain fun to shoot.
7.62mm (7.62 x 51 mm/overall 71mm) = M59 Ball, 150.5 gr bullet, 2,750 fps (838 mps)
5.56mm (5.56 x 45 mm/overall 57mm) = M193 Ball, 56 gr bullet, 3,250 fps (991 mps) (1in12 twist barrel) M16A1 rifle.
5.56mm (5.56 x 45 mm/overall 57mm) = M855 Ball, 62 gr bullet, 3,025 fps (922 mps) (1in9 twist barrel)M249 M16A2 and M4 rifles.
Round > Cartridge size > Bullet weight > Velocity > Energy
5.56 mm NATO > 5.56 x45 mm > 3.95-5.18 g > 772-930 m/s > 1,700-1,830 ft. lbs energy
7.62 mm NATO > 7.62 x 51 mm > 9.33 g > 838 m/s > 3,275 ft. lbs energy
MASS x VELOCITY = Muzzle Energy
The heavier bullet retains more kinetic energy at longer distances.