Is the Solid State Logic SSL 2+ MkII loud enough for the Audio-Technica ATH-M40x?
112.56 vs 113.20 dB/V — the M40x needs 0.745 V, the M50x 0.692 V. The SSL's 3.46 V puts them at 123.1 and 123.8 dB, with damping ratios of 35 and 38 against a published output impedance under 1 Ω. Electrically these are the same purchase.
On paper the M50x is "more sensitive": 99 dB/mW against 98. On the same output that advantage is 0.6 dB, and both headphones are 13 dB past the target anyway.
The M40x is 35 Ω at 98 dB/mW, the M50x 38 Ω at 99 dB/mW. Converted to volts they are 112.56 and 113.20 dB/V, so a 110 dB peak needs 0.745 V and 0.692 V respectively. Solid State Logic publishes +13 dBu maximum output level for the SSL 2+ MkII headphone amp, which is 3.46 V: the two land at 123.1 and 123.8 dB SPL, +13.1 and +13.8 dB of headroom. Both comfortable, and the difference between them is smaller than the step on most volume controls.
The pearl: the two differences partly cancel. The M50x has 1 dB more sensitivity per milliwatt, but it also has a higher impedance, and the mW→V conversion pays for that: 10·lg(1000/35) = 14.559 against 10·lg(1000/38) = 14.203, a loss of 0.356 dB. Net advantage per volt: 0.644 dB. Whenever you compare two headphones by their dB/mW ratings, you are also comparing their impedances without noticing — and on the milliwatt scale the M40x actually needs more power (15.85 mW against 12.59 mW) while needing more voltage too. The scale you compare on changes the ranking's size, not usually its direction, but here it shrinks it to nothing.
This is a source where the 1/8 rule can be checked, and it passes. SSL publishes an output impedance of <1 Ω. Against 35 Ω and 38 Ω that gives ratios of 35 and 38, where the rule asks for 8. Because <1 Ω is an upper bound, those are lower bounds — the real ratios can only be higher. In this batch only three sources publish the figure at all, and this is the one with the most room to spare.
So what does decide between them? Not the interface. The M40x has a 40 mm driver against the M50x's 45 mm and a different tuning; both take detachable cables and both arrive on 3.5 mm with a screw-on 6.3 mm adapter, which is what the SSL's 1/4" jack wants. Buy on the voicing and the earpads, and treat the sensitivity spread as noise.