Perhaps a touch esoteric, but with a center feed, the cartridge is presented to the bolt in the exact same spot each time. A Left/right feed presents the a cartridge to a spot that alternates every other shot. Center feed may allow a better fine tuning of extractors, controlled feed, etc.
However, since I am an ignorant, unwashed heathen, I'll continue shooting my Garand, my SMLE and my SKS. None of which is center feed, and do not seem to have significant feed reliability issues.