I wonder if gzip has improved? 15 years ago when I tested this, it was more efficient to gzip base16 encoded data than base64 encoded data. (At least, the English dictionary.) I assume that was because the 3:4 encoding broke up patterns in the source text and messed with the compressor.

But I just tested this again and it's not true anymore.

  $ wc -c american-english  
  971578 american-english
  
  $ gzip < american-english | wc -c  
  259977

  $ base64 < american-english | gzip | wc -c  
  429263

  $ hexdump -e '"%x"' < american-english | gzip | wc -c  
  478411