It's generally accepted that, due to licensing reasons, the pre-compiled Windows executables of FFmpeg come out of the box with lower-quality encoders – particularly when it comes to the default AAC encoder and the default resampler.
According to these sources, the solution is to compile the program from source:
FFmpeg supports two AAC-LC encoders (aac and libfdk_aac) and one
HE-AAC (v1/2) encoder (libfdk_aac). The license of libfdk_aac is not
compatible with GPL, so the GPL does not permit distribution of
binaries containing incompatible code when GPL-licensed code is also
included. Therefore this encoder have been designated as "non-free",
and you cannot download a pre-built ffmpeg that supports it. This can
be resolved by compiling ffmpeg yourself…
The Fraunhofer FDK AAC codec library. This is currently the
highest-quality AAC encoder available with ffmpeg. Requires ffmpeg to
be configured with –enable-libfdk-aac (and additionally
–enable-nonfree if you're also using –enable-gpl).
If you want FDK-AAC you have to compile handbrake yourself. I did it and the audio sounds great now.
I already have Cygwin available on my machine, and I'd rather use that to compile the program rather than setup another software ecosystem or burn a whole Linux distribution.
How can I use Cygwin to compile FFmpeg with better external libraries?