I actually have both. The metal would be harder to break if stepped on or dropped though.
Metal- long narrow feeders
Plastic-quart bottle chick feeders
I have only used plastic so far and no problems yet. I use a plastic tote filled with bleach water to sterilize them periodically, dunk-soak-rinse-air dry-back in service.
My feeder is wood, built by my father 40 years ago and used on the farm until he retired. Now on my 'farm' and catering to the girls just fine. The waterer is plastic with a heat element in the base to keep it liquid during our bitter winter. With all the concerns about plastic, I wish there was a heated metal waterer out there, but I haven't found any.
One aspect of the plastic feeders and waterers that I myself like is that the plastic tend to be a lot cheaper than the metal. At our local Tractor Supply Co, a 1 gallon waterer is about $12-$15, and the metal is around $25.
My feeder is metal and I haven't tried plastic feeders. My parrot and doves are using the little 1 gal plastic waterer, and I like it for ease of cleaning, using apple cider vinegar and being able to see the water inside, how much and if its clean. I have other friends that replace the base for that size on a regular basis due to breakage. My one experience with the larger plastic waterer has not gone well, and so far I like metal waterer better. I can feel for the weight to check water supply, not as handy as seeing it, but I expect the metal waterer to last a good while.