I'm no big expert on Zapdos, but I have utilized the big bird in the past. Zapdos, to me, was a pretty situational Pokemon to be honest. Sometimes it'd really pull its weight and be effective, while other times, it kinda lacked a bit and was almost like the dead weight of the team.
Zapdos isn't a bad Pokemon. But he's far from superb.
In my opinion, Zapdos would fall under the category of niche Pokemon. If your team struggles against certain Pokemon, and Zapdos is able to take them on all day, by all means utilize him. However don't expect Zapdos to always do his job. For example, he's no Skarmory or Blissey. Usually, these two defensive behemoths can be thrown in and are able to tank the majority of the metagame. Zapdos should only be used take on certain threats and shouldn't be used in a manner where he isn't successful.
TaBuu : Pokemon Legend