Carthage is not a versatile faction. With the Sacred Band Inf needing an awesome temple to recruit from, and the SB Cav needing an advanced stables, Carthage is limited to medium cav, and medium spearmen. Even the phalanx-using Poeni inf require an army barracks. Based on the troop limitations, it almost forces you to hire mercs, which is quite realistic. Spanish Mercs come in quite handy to balance out your spear based inf. And, of course, Rhodian slingers are awesome! Once you get the SB units, Carthage can steamroll just about anyone; especially if you throw in a few elephants! Fortunately, outside of Rome, Carthage has few formidable factions to face early on, allowing a build up of a stable economy from which to build higher echelon units.
I have never had a cav unit so all around effective as the SB Cav. They don't carry the shock value of Cats, but they are much easier to move around, and don't get bogged down nearly as much. The Companian cav comes close, with a better shock value, but I seem to lose more of my men from the CC than SB.