Single-shot .410 has very little kick, is light and easy to aim. However, it does not have much power or range. Could lack of range be an advantage from stand-point of safety?
20ga kicks much harder, esp. light single-shot models...do you really want to teach the kid to flinch from the start?
I am much in favor of .410 for kids or skittish adults...they can still do damage with slugs or BB shot, but without the kick that comes with much heavier 20ga OTOH, I tend to be a whimp...and most 12-13yr old kids I know who hunt or shoot trap use a 12ga.