Making reference to
Halo 4 Weapon Stats...
Due to the June Weapons update, the stats on LR hipfire make it entirely worthless against any precision weapon. You're forced to scope for practically every shot except for the fourth, which you can supplement with the burst feature for a headshot. BR does have more recoil, true, but that's only because it has burst mode in all circumstances. In that case, the DMR and LR would be equally as effective in regards to recoil management. People probably use the BR or DMR, because they are able to effectively use both hip and ADS fire in many situations.
Because the AR suffers from conic accuracy, while the BR is relatively linear in its recoil pattern. We can already rule out any distance that the BR cannot shoot 100% accurately to not be included in the test. From there it's a comparison to which kills faster, over what distance. Assuming you fire both guns as fast as possible, and there are no human errors (you're both standing still to test), everything should be controlled.
If you wanted to go about this further, you could compare theoretical Time to Kill values to see the percent loss in efficiency of the AR.
AR TKK: 1.20 sec
BR TTK: 1.43 sec
AR needs less than 83.9% of its shots connecting to become less efficient than that BR.