Easy. Please make sure to check their Tech tree, for a quick understanding of the rating.
Also assume that opponents are always of EQUAL playing strength and that everybody arrived to Iron without major problems.
I add some comments for where it does not sound so obvious.
1. HittiteObvious. That Tech Tree plus the Super-Cats will rock the game.
Their HHA is the best in the game, they have Armored Elephants, high-power SC, etc., etc.
The sea is not lost for them either, because lon-range galleys + fire galleys are still a very powerfull combo.
Hittites CAN lose to:
Persian that is being helped by food tribute (for super-fast Armored Elephants).
Egyptian, even alone, if the Egyptian knows how to use their strengths - SC, Elephants, Priests, ballista Towers and lots of micromanaging
Sumerian, if the Hittite's weapon mix is not adequate, for some reason. The mix against Egyptian and Sumerian is the key to winning / losing the game.
Against the Persian, if he manages the food (via tributing, that's how I see it) then Hittite is in trouble.
2. SumerianYes, the tech tree is way less impressive than Hittite's and they don't have metallurgy and Coinage, two key techs. But hey, their Cats are like semi-ballistas (due to inreased rate of fire) and shred everything. Plus, people keep forgetting how awesome the double farm production bonus is important from late bronze onwards.
Their clever use of healing Priests, Heavy Cats, War Elephants, SC and Ballista Towers will always make them very effective, no matter what.
Can lose to:
Hittite, at least in Cat wars and when the gold ends. In wood/food wars, they will win hands down (if they manage to erase the Hittite's farms, then their own will save them so much wood that they will be able to outproduce the Hittite in SC, which, albeit inferior, can win by superior numbers).
Note that the Sumerian is better apt to deal with Persian and any other Elephant Civs. Those Heavy cats almost behave like Ballistas, so...
RomanYes, the Roman tech tree allows them to make discounted farms and build very fast (due to the discount) and plant Siege buildings and Stables everywhere, then win by attrition with Siege versus Elephant / academy Civs and with SC versus the other Civs.
Civs like Egyptian (that have an edge against Hittite), Phoenician, Macedonian and Carthaginian all lose to Roman, due to Roman's Siege. The Combo Heavy Cat + helepolis is deadly, IMHO it is a frightening thing to face if you don't have super-catapults of your own.
Civs like Minoan or Greek, that have equally good Siege (and can produce the same type of Siege Combo) will lose to Roman because of not having the Scythe Chariots.
Loses to:
Hittite and Sumerian. Those cats are simply too much against Roman Siege weapons and they also have SC PLUS the nice Horse Archers. That's too much for a Roman to handle
The Sumerian is particularly costly to attack...
4. All others (except Shang, Yamato and Assyrian), does it matter which? Well, from here on, it's a matter of style, not power, all have their trump cards to play. each one may beat the others, if not facing any of the 3 Top...
IMO, those 3 are the summit in Iron.
And don't forget that, in team games, a Yamato that goes super-fast to Iron can make Hordes of HHA and be a hell of a helper to the other, more "heavy" Civs!...
I'm talking here about the Civs with the "major" role in the game, ignoring the power of the "weaker" ones is silly.
Example: A Macedonian Armored Elephant wave can be backed up by his Carthaginian partner's Helepolis.... This is another very effective combo. You can make more of these with different Civs.
Combined arms works well also with Combined arms + Civs!...