okay first off any civ with horse archers will beat persia in iron. Non-ballistics catapults, short range horse archers/towers and the worst economy in the game assures this. Also any civ that gets helepolis is better than persia since persia can't do much against them, again non-ballistic catapults just aren't going to do it, especially when you are building them with only 1 upgrade. Any civ with elephants and good priests will beat persia, since persia has more problems killing priests than any other civ probably, and fast elephants don't win battles against slow elephants, espeically when you are getting food for them without any upgrades.
As to the navy being good, it isn't, 1 wood upgrade = half as many ships = dead persian.
Lets take a look at persias iron for a second...
barracks- this is actually persias strength in my opinion, 3rd best legions in the game. Though you'll have fewer than phoenician so in practical terms they are the 4th best.
stable - fast elephants, these are nice but they still die to the same thing regular elephants die against and persia general makes fewer than another civ could, they also get the heavier cav but its useless without coinage. Basically average stables IMO and its supposed to be there strength.
Temple - okay priests, all techs, no coinage, no chariot archers to take out others priests, no good way to protect there own. Lots of civs with better temple.
Docks - great triremes, aweful wood cutting, expect to lose the seas against a good player, you just won't be able to build as fast as them, I'd say average docks.
Towers - short range guard towers, outranged by normal civs archers. These are posibly worse than yamato and minoans towers in iron, below average towers.
Siege - ballisticsless catapults, no helepolis, I'd say even civs with fully upgraded stone throwers are better. Poor siege.
Academy - none, worst in game obviously.
Archer range - short range composites, HA, elephant archers, average archer ranges, lack of coinage rears its ugly head again, you'll run out of gold fast if you go all out HA. I'd say average ranges at best.
Economy - easily worst in game, missing 2 wood upgrades, 2 farm upgrades and the wheel, not to mention coinage and siegecraft.
So basically they are below average in almost every catagory except there 2 best, where they are average, add in the crappy economy and you have the worst iron age civ in the game.
Tell me which civ you think they can beat in iron with even numbers of villagers and I'll tell you why I think your wrong.