somebodyelse
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Based on a quick search we have:
Audeze MM-100: 18Ω 98dB/mW
Ananda Nano: 14Ω 94dB/mW
From the review here we have an output impedance of 11Ω for the 6.35mm output, and a comment that the 3.5mm is supposed to be lower. The output impedance forms a potential divider with the headphone impedance. Given the low impedance of your headphones, the lower impedance of the 3.5mm will lead to a bit more volume than from the 6.35mm, explaining your preference in blind testing. Planars usually have a relatively frequency independent impedance as @fin says, so the output impedance probably wouldn't change tonality.
The review shows the Babyface Pro FS has pretty good noise and distortion performance (you are unlikely to hear a difference) - its real drawbacks are available power output and output impedance. We've addressed the output impedance above so the question is whether it has enough power - headroom is just whether it has enough power to cope with peaks above your normal listening level. What that level is depends both on your normal listening level, and on how dynamic the music you listen to is, which is why I asked how far up you needed to turn the volume. The rule of thumb for classical music (relatively high dynamic range) is ~20dB headroom. Mainstream normalisation targets have less than this (13dB for YouTube, 14dB for Tidal last I checked - they sometimes vary a bit) and loudness wars victims even less. If you apply EQ you may need to allow a bit more - the pre-gain setting should be a good guide.
We don't know power output with the 3.5mm connector with your headphone load, but we can make some rough assumptions. Using the lower sensitivity Ananda Nano and taking the power from the 33Ω test with the 6.35mm output, putting the numbers into one of the online headphone power calculators (say this one which shows the formula it uses) you get peaks of 111dB without clipping. With 20dB of headroom that puts listening level at 91dB which has a safe exposure time of 2hrs. I rarely listen that loud, so for me there would be no benefit getting a separate headphone amp. Others like to listen louder (for a short time I hope!) so would see a benefit. If you're not pushing volume near maximum you're probably like me and don't need a more powerful amp.
Audeze MM-100: 18Ω 98dB/mW
Ananda Nano: 14Ω 94dB/mW
From the review here we have an output impedance of 11Ω for the 6.35mm output, and a comment that the 3.5mm is supposed to be lower. The output impedance forms a potential divider with the headphone impedance. Given the low impedance of your headphones, the lower impedance of the 3.5mm will lead to a bit more volume than from the 6.35mm, explaining your preference in blind testing. Planars usually have a relatively frequency independent impedance as @fin says, so the output impedance probably wouldn't change tonality.
The review shows the Babyface Pro FS has pretty good noise and distortion performance (you are unlikely to hear a difference) - its real drawbacks are available power output and output impedance. We've addressed the output impedance above so the question is whether it has enough power - headroom is just whether it has enough power to cope with peaks above your normal listening level. What that level is depends both on your normal listening level, and on how dynamic the music you listen to is, which is why I asked how far up you needed to turn the volume. The rule of thumb for classical music (relatively high dynamic range) is ~20dB headroom. Mainstream normalisation targets have less than this (13dB for YouTube, 14dB for Tidal last I checked - they sometimes vary a bit) and loudness wars victims even less. If you apply EQ you may need to allow a bit more - the pre-gain setting should be a good guide.
We don't know power output with the 3.5mm connector with your headphone load, but we can make some rough assumptions. Using the lower sensitivity Ananda Nano and taking the power from the 33Ω test with the 6.35mm output, putting the numbers into one of the online headphone power calculators (say this one which shows the formula it uses) you get peaks of 111dB without clipping. With 20dB of headroom that puts listening level at 91dB which has a safe exposure time of 2hrs. I rarely listen that loud, so for me there would be no benefit getting a separate headphone amp. Others like to listen louder (for a short time I hope!) so would see a benefit. If you're not pushing volume near maximum you're probably like me and don't need a more powerful amp.