I figure you could probably just dump some water or use a fire extinguisher on the Phoenix while it is regenerating, that or pull a Conker's Bad Fur Day and just extinguish the flame with your bladder full of beer.
Seriously though, the Phoenix would kick the shit out of the Centaur. The Phoenix has a long history of being an awesome mythical creature, and the Centaur exists because some human decided he wanted to put his penis into a horse.
Would you rather bow down to some horse fucking ancestor or some mystical fire bird! Yeah, that's what I thought.