Physically Samurott has Swords Dance, Megahorn and Torrent over Azumarill, which is pretty significant. He also has 110 base Special Attack, although it rarely sees use in UU. Megahorn is huge, though, as it gives really good 2 move coverage with Waterfall (making it easy to run Aqua Jet and Waterfall on the same Swords Dance set) and it destroys solid Azumarill counters such as Slowbro and Tangrowth at +2. Even though Samurott's Water attacks don't hit as hard as Azumarill's (or Feralgatr, who is perhaps a better comparison), having a stronger coverage move to hit Grass- and Water-types and access to Swords Dance means that often it is much harder to wall. Samurott is also faster, which helps when sweeping.
They each have their advantages, but Azumarill can't be said to outclass Samurott, as their differences tend to leave them playing very different offensive roles (sweeper vs. wallbreaker).