The pattern is what kills, and that results from the interplay of the boring of the barrel and the cartridge (meaning the wadding, shot-charge and shot-size).
In theory, you can check the tables of percentage of charge for a given choke put in the magic 30" circle at a given range, and from the charge and shot-size calculate how many pellets that puts there.
Bore-size should have nothing to do with it, though it has been suggested that higher-pressure loads (e.g. 3" .410 cartridges) might give worse patterns than lower-pressure ones.
The best way to check it is to shoot at a pattern-plate or similar, and see what happens.
As I see it, the 24g 7.5 20bore cartridge for smaller quarry, and the 30g 5s for larger give a marked advantage over anything the .410 (smallest shot-size 7, if you're lucky) has to offer.