Hardware acceleration in Adobe Media Encoder vs ffmpeg
Media Encoder and ffmpeg should generate the same quality if given the same encoding parameters.

GPU encoders are provided by GPU vendors. I haven't heard of any third-party implementations. The possible differences lie in the wrappers i.e. the code which initializes the encoder parameters, and written by the interfacing app. There, I would expect ffmpeg to offer more fine-grained choices although I haven't look at AME's offerings as of late.