James is right. In the strictest sense, BB's are plastic (certainly by definition of the process). However, there is a world of difference between, say, a plastic water bottle and a Better Bottle.
BetterBottle® fermentation carboys are: are: 1) Designed to be strong, scuff resistant, easy to handle, and essentially unbreakable, 2) Pure – Taste- and odor-free, BPA-free, DEHP-free, and plasticizer-free, 3) Virtually impermeable to oxygen, 4) Clear and colorless, 5) Incredibly light weight, and 6) Extraordinarily easy to wash and sanitize (no brushes necessary). BetterBottle carboys are not at all like other plastic carboys. The special PET, used to make BetterBottle carboys, is non-absorbing, non-porous, and non-wetting (hydrophobic), so it will not carry over flavors from one batch of wine or beer to the next and it is easier to clean and sanitize than glass or other plastics.
You notice they refer to it as a fermenter carboy, not a bulk aging carboy. To me that means fermenting (alcoholic and MLF), and maybe initial clearing. IMO, they are not meant for long term bulk aging.
One other nice thing about a Better Bottle is it can expand and contract without necessarily expelling or inhaling gas through the air lock. This can cut down on the intake of air when the pressure increases outside the carboy.
Wine Maker magazine did a story on some testing of solid carboy bungs. They are not as well sealed as one might think. There is a lot of air (gas) leakage around it when the pressure outside changes.
A BB will reduce this leakage because the bottle itself can better expand and contract with pressure changes.
I do however prefer glass because I like to use my vacuum pump for degassing and racking. I have found that one should always remove the solid bung from a filled BB before moving it. It tends to want to pop out when the bottle is slightly squeezed.
As JohnT pointed out, a wooden frame built permanently around a glass carboy is a nice thing to have. So many carboy breaks are due to seemingly incidental contacts with other carboys or anythng else that might come into contact with it.