I’m thinking about other apps that have an addictively competitive quality to them (DuoLingo, Waze, Words with Friends), and one thing they all have in common is some way to mark your progress beyond the individual session, and a way to compare your progress with others. This could be accomplished in a lot of ways. I think badges would be one good way to accomplish this: a badge for your first 5/10/20 verses memorized, for your first 7 days of use, for reviewing old verses with no errors, etc. You could accomplish a similar thing with levels, but I think badges might be more fun
Also having a way to compare progress within a group, and/or an overall leader board might encourage younger users.