Marill gets more Egg Moves in every game. Sword and Shield are also the only games where Azurill gets Belly Drum, Aqua Jet and Perish Song. It also can't learn any of these moves in previous Gens. Marill can also breed to get all 3 of those moves in every Gen except ,2 and 3, and in those games, it gets Belly Drum and Perish Song. There is no reason to breed for Azurill unless you want something cute or to complete the Pokédex. Also, looking through their Egg moves, it looks like Marill gets All the Egg moves Azurill does plus more.
Hope this helps!
Source: These Pokémons Egg Move pages