The 5.56mm (.223 caliber) was designed to provide a combination of low recoil, reasonably accurate full auto, good accuracy, light weight, and lighter weight ammo. It had some teething problems when it was issued as the Army changed the powder type, which combined with the more relaxed cleaning requirements of the M14 led to a lot of jamming. The Marines wanted better long range capability and the result was the M16A2, which seems to almost weigh as much as the M14 that it replaced. They replaced the full auto with a three round burst mode, added a heavier barrel and used a heavier bullet. Marines have reported that it's the most accurate weapon that they've used, even compared to the M14. The M14 (7.62mm NATO, which is the .308) is a premier long range weapon in a match rifle, but the M16A2 seems to be more consistent as an issue service rifle. One sees the M16 and the civilian equivalents on highpower ranges, shooting out to 600 yds, while almost none of the much talked about SKS/AK/HK rifles are seen.
The 5.56 is popular among Alaskan natives as it'll get the job done with good shot placement, ammo is cheap compared to other centerfire cartridges, and it has low recoil. I remember considering a heavy barrel AR15 for target shooting, but declined as it seemed real expensive at something like $600. That was obviously awhile ago.