While trying carthage i noticed that out of three embassies,which have different costs, 1 of them isn't equal in terms of value to the others. So lets evaluate them one at the time.
While all 3 offer u a swordsman unit each, a unit that is simply put of the best in game, the italian embassy also gives you a spear cav unit, the campanian horseman, a meh unit. This wouldn't be a problem necessarily but coupled with the 100 metal cost of this building makes it problematic.
The iberian embassy costs 100 wood and 100 stone Which is more in line with a normal barrack. But with this building u get a javelineer cav, again one the better units in game. A good unit selection balanced with an increased initial cost.
Finally the Celtic embassy has a standard 200 wood cost nd offers you 2 units like the rest, a swordsman and sword cav, which one can argue that it is a bit redundant but still these are the best melee fighters in the game. The cost alone makes this building spammable.
In conclusion, the iberian and celtic embassies are fine but the italian embassy leaves a lot to be desired.