Both mean "again" with shades that make sense in some context and don't make sense in others.
СНОВА can be used with an additional shade "anew" (from the beginning).
ОПЯТЬ has a connotation of repetition with no significant change. If that's not what you want ("eh? Could you please say that again?"), better reconsider and use "ещё раз" (another time, one more time).
Otherwise they can double each other.