What they share
Both are Latin in origin and both draw from celestial vocabulary. Both are now firmly mainstream after a long rise through the 2010s. Both have strong namesakes (Aurora from the Roman dawn goddess, Luna from the Roman moon goddess).
Pick Aurora if…
Pick Aurora if you want the longer, more ceremonial option. Aurora means 'dawn' in Latin and carries a full, literary weight. Rory as a short form gives you a playful alternative for everyday use.
Pick Luna if…
Pick Luna if you want the shorter, more immediate option. Luna means 'moon' in Latin and lands with a soft, unassuming confidence. It does not typically shorten; it is already complete.
Aurora is the grander pick; Luna is the quieter one. Both are unambiguously celestial names, which is rare. If you love both, consider whether you want your child's name to announce itself (Aurora) or hold its weight quietly (Luna).