Well, since both of your Politoeds have the Adamant nature, you basically want an ability that is either a best match with the nature, or just overall.
With the Damp nature, it prevent the use of any self-destructive move (this also includes the ability Aftermath). If you look overall, only 90 Pokemon can learn Explosion/Self-Destruct, (+4 if you include Drifloon/Stunky + evos). So overall, you have merely a 12% of battling a Pokemon(s) who will benefit your Damp ability - with Golem or Electrode being the most common. But these will most likely be the case of in-game battles; it's highly unlikely you will end up battling Pokemon with Explosion, Self-Destruct, or Aftermath in a PvP battle.
With the Water Absorb ability, it takes Politoed's 0.5x resistance, and makes it immune to Water; and granting 1/4 max. HP in return. With this, there are over 30 water moves, and over 100 water Pokemon - not to mention you don't have to be a water-type to learn water moves (excluding some Pokemon). This ability can be very beneficial in doubles/triples with a ally learning moves such as surf. With this, you can attack, and heal the ability bearer at the same time. Otherwise, you can use another water move or hope the opponent will use one.
So overall in my opinion, I would definitely chose a Politoed with Water Absorb > Damp. Unless you have the hidden ability Drizzle, I would recommend that one instead - but that's a different story.
Your Choice! Hope I helped! :)