Zapdos as a generalist

You will be struggling against pokemon that Raikou doesn't have any trouble against, like Lapras, Walrein or Omastar.

What bothers you when using Zapdos is many water type Pokemons learn Ice type skills such as Blizzard. Against Ice+Water type like Lapras, Zapdos is never a safe bet. You also have to avoid Rock type, while for Raikou it is not necessary (unless opponent is Ground+Rock type). Rock+Water type such as Omastar will be troublesome for that.

So as a gym generalist, Raikou is definitely better. Can't say Zapdos is bad though. It's still strong Pokemon with few weakness and useful attack type.

I think Zapdos can be comparable to Raikou in Raid sometimes. When you deals with Pokemon like Ho-Oh or Lugia, Zapdos's Flying type will give it an advantage against skills like Solar Beam or Sky Attack.

Thunder Shock charges energy fast and allows for good dodging. Wild Charge is an awesome move.

Charge Beam is weaker and slower making dodging harder. Thunderbolt is a good move, but not exceptional.