Zap Cannon does the most Damage per use, but Thunderbolt is far more useful and does almost the same DPS over the course of a battle. The dodge timing is easier for TB, so you can get more of them off safely = more eDPS (effective DPS). If Zapdos had some better quick moves, I'm pretty sure he'd be the best period. I'm not sure who's better in the electric spot at the moment, but stats-wise it should be Zapdos. Zap has higher attack stats (the only stat that matters on a legendary), the same Stamina, and a bit less Defense. Which might actually be useless (or the least useful) on legendary mons, as you can't defend with them.
Raikou get's access to better moves. Wild Charge and TB are great. His typing leaves him less vulnerable to double weakness, but he also doesn't get as many STAB opportunities (3, compared to 6 for Zapdos) and the extra type coverage only hurts against Rock (but again, you'll be attacking INTO pokemon, meaning you'll know what type you're going to face)
As it stands, the double typing is a benefit for Zapdos. Basically giving him twice the resistances of Raikou (6 instead of 3) and only giving him one more weakness to gain those bonuses (rock + ice instead of just ice). There's all the info, hope you make a good choice and keep your best.
For a TLDR:
Zapdos is better for his role (electric attacker)
Raikou get's better moves, and has one less type to exploit, although this is irrelevant in the current metagame.
EDIT: Found a good screenshot that explains this.
Zap Cannon does 140 on paper
Thunder does 100 on paper
ZC has a cooldown of 3.7 seconds, meaning you can't dodge until those 3.7 seconds are over.
It uses 100 energy
DPS = 37.84
(Cooldown divided by damage, or how often you can use it vs. how long it takes to use)
Thunder has a cooldown of 2.4 seconds
It uses 100 energy
DPS = 41.67
This is because you can fire off a Thunder much faster than you can fire of Zap Cannon. Meaning you recover and start attacking/dodging sooner, which equates to more energy buildup, which = more damage.
Hope that makes things crystal clear!
Oh and Raikou can't learn Zap Cannon. He has Thunder, Thunderbolt, and Wild Charge.