And JPG is a lossy image compression that is VASTLY inferior to PNG (or GIF) where crispness of text and graphics need to be preserved - half a flaming megabyte each... I thought they were slow to load!

Frequency plots are good at showing lowpass and artefacts in the frequency domain, but tell you little more about the actual fidelity.

Direct waveform comparison also tells you next to nothing, as it does not jusge the significance of what has been lost or added.

In general, most lossy compressions are juggling:
1. Lowpass
2. Loss of lower level sounds, hopefully below ATH and masking level
3. Occurence of artefacts, such as pre-echo, distortions

A/B testing is the only reliable way, and with A/B, there is often another parameter that would be taken, an assessment of the quality / irritation factor of the version cleary though to be inferior. Like looking at a load of TVs set up in a store, the pictures are often quite different (an A/B fail), some are clearly poor (noise etc.) but you maight choose one that is actually not the best fidelity to the original.
I use that example, as most people are better at judging picture differences than audio.