Analysis of Politoed and Poliwrath
VS 
Stats Comparison
HP | ATK | DEF | SpA | SpD | Spe
Politoed : 90 75 75 90 +100+ -70-
Poliwrath: 90 +95+ +95+ -70- 90 -70-
As we can see, Politoed and Poliwrath share the same base HP and are equal in Speed as well, but this is where the resemblances stop. Poliwrath is obviously bulkier in Defense, sitting at 95 base stat which is not bad at all, given its excellent Water / Fighting, and same can be said about his Attack stat which is also 95 base. In contrast, Politoed has 75 in each, making it physically weaker than its alternative Poliwrath. However, when Poliwrath shines physically defensively, Politoed shines specially defensively, boasting better Special Attack base of 90 and Special Defense base of 100, the two being superior than Poliwrath's meagre 70 and decent 90.
We can deduct of this that Politoed is more adapted in the Special domain than its alternative Poliwrath is, while that latter is better in the Physical domain than the former.
Movepool and Typing Comparison
Pure Water-type has proven to be excellent defensive, having resistance against common Fire-, Ice-, Water- and less common Steel-type and weakness to Electric- and Grass-type Attacks which are rarer than other types.
Add in Fighting-type for a bunch of new resistances for new weaknesses. Bug-, Rock- and Dark-type attacks are resisted along with Fire-, Ice-, Steel- and Water-type attacks, by Poliwrath; 3 resistances in exchange of 2 new weaknesses to Flying- and Psychic-type attacks.
Politoed takes the safe path of having 1 type, 4 resistances and 2 weaknesses; while Poliwrath takes the riskier path of having 2 types and 2 added weaknesses for a total of 4 weaknesses, it makes up for having 7 resistances. It's a matter of opinions mainly, but Poliwrath has the better typing in my opinion.
As of movesets... there are not so many differences. Both of them get Poliwhirl and Poliwag egg moves. However, at level 1, Politoed gets Perish Song while Poliwrath gets Circle Throw and Submission. Politoed can learn Bounce and Hyper Voice by leveling up and Poliwrath gets Dynamic Punch and Mind Reader. Poliwrath's movepool is slightly larger than Politoed's movepool too.
The Verdict
You said Water Absorb, right? Poliwrath is your man. Politoed's popularity comes specially from Drizzle access and without Drizzle, Politoed isn't worth much. Poliwrath's superior typing, slightly larger movepool and better overall bulk of 90 / 95 / 90 wins over Politoed.
The Movesets for each
Politoed is better known for its Ability, Drizzle, which summons Rain. It will give a good boost to Water-type Pokemon and to Pokemon that have rain-friendly Abilities. Politoed's only role is a Support Pokemon. If you are using anything else, then you're using Politoed wrong, maybe except for Perish Song Politoed which I dislike personally.
Movesets:
Politoed @ Damp Rock
Ability: Drizzle
EVs: 248 HP / 164 SpD / 96 Spe
Careful Nature
-Scald
-Toxic / Hypnosis
-Rest
-Encore / Rain Dance
Politoed @ Leftovers
Ability: Water Absorb
EVs: 252 HP / 252 Def / 4 SpD
Careful Nature
-Perish Song
-Scald
-Toxic
-Protect / Encore
Poliwrath, on the other hand, can fulfill 2 different roles and is blessed with a good typing but the Hidden Ability he has, Water Absorb, is absolutely mandatory except if you can backup your Poliwrath with Rain support, where Swift Swim will do fine.
Poliwrath @ Leftovers / Choice Specs
Ability: Water Absorb
EVs: 96 HP / 252 SpA / 160 Spe
Careful Nature
- Scald / Hydro Pump
- Focus Blast
- Ice Beam
- Vacuum Wave
While Poliwrath isn't exactly what you would expect to turn out as a Special Attacker, he can do surprisingly well in lower tier and will do surprisingly bad anywhere higher.
Poliwrath @ Leftovers
Ability: Water Absorb
EVs: 252 HP / 252 Def / 4 SpD
Careful Nature
- Circle Throw
- Scald
- Rest
- Sleep Talk
The more defensive version. Your bread-and-butter ResTalk Circle Throw.
