I won't call it the Group of Death (that would be Russia/Tamil/Arabia or Spain/Prussia/Greece), but it's quite close.
UP: Moors > Egypt > Carthage
Moorish UP is one of the strongest and most interesting in the game. But it expires rather early. Carthaginian UP is very situational and will be completely changed/removed with the removal of mercenaries.
UU: Carthage > Moors > Egypt
None of the UUs is very unique at all so they are ranked according to effectiveness.
UB: Egypt > Carthage = Moors
Too close to call, but Egyptian UB works best with their terrain and UHVs. And it's more unique than the other two.
UHV: Carthage = Moors > Egypt
Again very close, but 2 of Egypts UHVs are cultural - they feel repetitive, especially the 2nd one which offers very little challenge.
AI performance:
Too close to tell. All expand historically but can't offer to much resistance to Human players (of Rome/Greece/Spain).
In the end my vote goes to Moors because they don't have obvious weaknesses like the other two (Egyptian UHV and Carthaginian UP).