A pellet from a 410 is as effective energy wise as one from any other gauge.
The pellet count is with no 4s approx 140 per oz the 410 will have between 1/2 and 3/4 oz in the Shell, the 20 gauge 1 1/4 typically so the pattern will be twice as dense. 410 guns are light and suited to small frame persons but put magnum loads through them and it defeats the purpose.
The 20 may be the only shotgun he ever needs, whereas the 410s limits will sooner or later be realised.
At the range limit you say either would be suitable in my opinion
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