Can Media Encoder (or any other Adobe application) perform functions that ffmpeg and Handbrake do, regardless of whether it takes longer or uses more resources, etc.?
I'd say it's better than both, but try it for yourself and report back.
Can you be more specific? What ffmpeg or Handbrake functions are you looking for?
Can AME add toggleable subtitles to a file like Handbrake can? No.
Can AME natively export H.264 using x264? No.
AME can export to many more formats than Handbrake.
With a simple line of code ffmpeg can easily combine an audio stream and a video stream from one file into a new container without encoding a new format.
Those four things are pretty different from one another, so what is it that you're hoping the Adobe apps can do?
AME cannot handle VFR.