Azumarill is the better option, here's why
Azumarill has early accesability, having Huge Power as an ability combined with it being able to learn some good solid Water type moves not to late into your journey such as Aqua Tail at level 21 that can later be replaced with Waterfall, access to Ice type moves that can do some good damage equipped with a NeverMeltingIce or an Ice Gem, and it also has access to some good HM Moves that it can also use in battle with its solid ability.
Azumarill @ Mystic Water
Although Swanna is helpful especially when your able to get it before the 5th gym with good mixed attacking stats and access to Fly to help you move around the region the main problem lies with its late evolution as unlike Azumarill, it evolves late and with poor stats its not worth it and there are other better Flying type options such as Crobat or Sigilyph, although if you want here's a moveset for it.
Swanna @ Mystic Water
I would say go for Azumarill as early accesability and better stats is really good but make sure to get an Azurill with Huge Power then evolve it before it gets to level 20 were it will have good Water Type STAB to use until it gets Waterfall later on in the game, Hopefully this helps :)