Both aeroponic and hydroponic systems use a lot of plastic parts, although aeroponics may have an advantage there. Aeroponics setups may have a slight advantage because the physical configuration requires less tubing and hoses, lowering their carbon footprint.
A relatively new option for all types of controlled environment growers is bioplastics. The plant based polymers used in bioplastics are free of hydrocarbons and environmentally friendly. They are part of a developing industry and are still not very widely used, but many parts of your system could be built or replaced with bioplastics to make your setup even more sustainable. If you're looking at a prebuilt system, ask your supplier if they'd consider make a truly green product.