This test isn't very informative because both .png and .jpg are already compressed formats, with "better than gzip" strength so gzip/deflate isn't going to be able to compress the underlying data.

You only see some compression because gzip is just backing out some of the redundancy added by the hex or base64 encoding, and the way the huffman coding works favors base64 slightly.

Try with uncompressed data and you'll get a different result.

Your speed comparison seems disingenuous: you are benchmarking "xxd", a generalized hex dump tool, against base64, a dedicated base-64 library. I wouldn't expect their speeds to have any interesting relationship with best possible speed of a tuned algorithm.

There is little doubt that base-16 encoding is going to be very fast, and trivially vectorizable (in a much simpler way than base-64).