They were exceptionally good cavalry in that region, the Numidians. But this was more because there really was not anybody else to contest them on the battle field. Rome was an infantry fighting force, and although it did have some cavalry the focus was always on infantry tactics and there were only a few hundred horse per legion, whereas there were optimally 6 thousand foot.

Carthage was a mercentile nation, not a militaristic one like Rome. Carthage's own army was small as their focus was naval trade, exploiting their wonderful geographical position. So Carthage's armies were mostly made up of mercenaries. What mercenaries were nearby that had plenty of horses? Thats right, the Numidians. Scipio Africanus realised that Carthage's use of the numidians was a major advantage over Rome, so he endeavoured to win the support of the Numidian leaders Syphax and Massinissa. He eventually won over Massinissa, and after the burning and pillaging of Syphax's camp, he ended up with the best cavalry force as well as the best foot soldiers. So ended Hannibal.

So basically, the Numidians were the only people in the western Mediterranean who had a large equine culture. Carthage and Rome did not.