I just did a test scenario with Persia, Rome, Celts, and a 4th "wildcard", Carthage. I gave them equal land (10x10grid, all bonus grassland), and put chokepoints between each area so that I could block them with a modded unit. I let them attack each other (after they were fully developed) in a play-off fashion.
Rome vs. Celts -
They both had 100 UUs going into the battle. Rome looked like they were getting the upper hand for awhile (defeating many Gallic Swords and Celtic spears - they love building those things!). But, Rome eventually lost.
Persia vs. Carthage - Really no contest here. After Carthage's sneak attack (100+ Numidian Mercs, and 76 swords), Persia was all over them like a swarm of angry bees.
Championship Match
Persia vs. Celts - It was a stalemate for the first couple of turns (Celts 440 Gallics to the Persians 400 Immortals), with the Celts actually losing ground a little bit. Then came the Celtic Spears. The Immortals were so busy attacking the swarm of units, that the retreated Gallics were able to heal, and come right back in. It wasn't long before the Celts made a swift advance.
Conclusion?
The Celtic civ as a whole is the best suited for the ancient era. Reason? Mobility. In the Persian war, it seemed like 1/2 of their troops retreated. That's like 100 out of 200 that the Persians could have defeated. Same was true with the Romans. The Celts were also able to quickly reach problem areas, unlike the Persians, or Romans.
The one thing I noticed though, is that the Celts were the only ones who used 350 spears enmasse as one huge pillaging machine. That might have played a part in it too, but that wasn't what this scenario was about. It was seeing how the civs do in a normal game with equal starts. (Also, ships were taken out in this test, as well as wonders). This was done on Regent level to give the AI a normal build time. (no bonus/penalties)