Empirical results. I own both headphones and have used them on multiple sources including my phone, laptop, DX3 pro and Benchmark HPA4 among others.
The 58X plays notably louder for the same volume setting and sounds less compromised by weaker sources. Due to the impedance differences the K712 will draw more than twice the power for the same voltage. If the headphone sensitivities were rated in mW then the 58x would be 3-4dB more sensitive.
For reference I've found the K712 to have a similar loudness to my HD600 which Sennheiser spec at 97 dB (1 V).
FWIW from the DX3pro I often prefer the K712 for its more precise, explicitly detailed, punchy and spacious sound (more exciting) - but the somewhat more relaxed, fuller sound of the 58x is also appealing and probably more 'correct' and long term listenable.
I'm comparing both while typing this - they're quite different but I like whichever I'm listening to.
Edit: I don't want to give the impression that the 58X is super sensitive - for example its nowhere near the sensitivity of the my K371 (AKG spec at 114 dB SPL/V), and I would rate that HP as very easy to drive. The AT headphones are also very easy to drive.