I usually play Zeus, but I've always had pretty good luck with Poseidon against Egyptian players. If you are Zeus, however, you still stand a very good chance. If you can get to Mythic before them, they can be very screwed. Nothing decimates an Egyptian's morale like seeing 5 of their expensive War Elephants turn to stone thanks to Medusa. If you chose to go with Hephaestus, you still have a good chance. You should have maxed out armor upgrades thanks to Heph's special armor techs, plus your faster myth gather rates and capacity will help you churn out Colossi like no tomorrow. Colossi are one of the few Myth units that actually have two upgrades that pertain only to them. Just sending a Colossus with a few cavalry to raid your opponents gold can be surprisingly effective. Especially when he starts to eat their goldmine ;-).
Quoted from Numenorean 7:
I play Eggy a lot, and I like it when my opponents choose Greek. The Greek gods have obvious strengths, so you build slingers vs. Hades, axemen vs. Zeus, and spearmen vs. Posiedon. If he sends in a counter unit, then he's just given up his god's human bonuses.
I don't think it's that simple. Peltasts, for instance, become available in Heroic and are probably a Chariot Archer's worst nightmare. The Greeks are usually at a disadvantage because of all the buildings they need to build. Whereas an Egyptian can build 3 units out of one Barracks, the Greek player needs to build 3 buildings. However, once Heroic comes along, the Greek usually makes up for this disadvantage by now being able to build 6 units out it's (hopefully) pre-existing buildings. As a Greek player, I usually end up building 2 Archery Ranges, 2 Stables, and 3 barracks right before advancing to Heroic (in ADDITION to my pre-existing base). It doesn't cost any wood to advance, and a smart Greek player always has plenty of villagers on that resource. Come Heroic, I usually build a triad (1 Acad, 1 Range, 1 Stable) by each TC I claim, and even more by a FB.
You may not believe it, but you don't have to be Poseidon for a Hippikon to cause problems for a Chariot Archer :-). Really, it's all about having enough buildings to create and replenish an army fast enough. If the Greek player does that, he's in a good position.
Hades, of course, has strong buildings. Which can usually withstand Ancestors, if some army is backing them up. You definitely want archers against ancestors. With Hades, going for Artemis is almost always a good idea, and its arguably the most destructive Greek GP that exists (of course, Isis' Monument bonus is a problem, but by Mythic you should have a few Gastraphetes to take care of them). Ranged civs, whether in AoK or AoM, are always dangerous for villagers. If your army is losing to them, it's only going to get worse when 20 Toxotes and 15 Peltasts obliterate your 16+ villagers at a gold mine before they can run away.
Poseidon has cavalry bonuses, which if done right always seem to bother Egyptians more than other civs. Plus he has militia, which almost always stop any Egyptian who doesn't decide to boom. Poseidon is almost like the Norse in a way, very difficult to successfully raid, and also an excellent raider. DeathAndPain would tell you that a rusher destroys a boomer. As someone previously mentioned, Ceasefire accompanied with a great minor godpath is all you really need.
Sine AoM:TT 1.03, I never really felt disadvantaged as a Greek player, against any race. You just need a good starting BO and you are set. The rest depends on how well you adapt to certain situations, and how experienced of a player you are.