I think Drapion belongs in Low tier. He comes late, shortly after the 6th gym, and while he's never particularly weak, he isn't very strong either. He has a wide movepool, and decent Attack and Speed, but his moves have low power. Now, he filled a need for my team, in that he had a STAB Dark type attack for Ghosts and Psychics, and he performed great against that. However, I didn't find myself wanting to use him much until Victory Road and the Elite 4, and he did great there. But in the meantime, he provides little besides a non-STAB Ice Fang against the Opelucid Gym. Toxic Spikes could have been a neat utility move, but there's just no one worth using it against. Overall, he just came late and was thoroughly mediocre until Victory Road. I did not try using Hone Claws, though. I found myself wishing he had Swords Dance quite often.
On a side note, about Azurill, mine didn't evolve until level 21. I was pretty careful with training, I tried not to let it die, but I think this was a result of ditching my starter for i as soon as it could handle itself in combat. Even still though, it could contribute perfectly fine with Return and Dig coming off it's ridiculous attack, until I could access the move relearner.