I hope it is correct, what I found to this topic on the internet.
I needed to look because I had up to now no demand for research on this topic.
As I regarded this topic as interesting, I had a look and hope that I do not summarize it wrong. Otherwise sorry
But maybe you can prove this yourself now where you know where to look for.
Careful: compare at equal volume levels, louder sounds better and you might have a bias (psychoacoustic).

Your headphones all have relatively low impedance, ranging from 32 to 37 ohms. For simplicity, let’s assume an average impedance of 35 ohms.

With the 6.3 mm output (10 ohms), you would achieve a damping factor of: 35 ohms / 10 ohms = 3.5
With the 3.5 mm output (0.1 ohms), the damping factor would be 100 times higher: 35 ohms / 0.1 ohms = 350

It’s generally recommended to aim for a damping factor of at least 10 for headphones, meaning the output impedance of the headphone amp should not exceed: 35 ohms / 10 = 3.5 ohms.

So, when you have two outputs to choose from—one with 0.1 ohms and one with 10 ohms—the 3.5 mm output (0.1 ohms) will likely provide better bass control due to the much higher damping factor.

What does a higher damping factor improve?

— Tighter bass response: A higher damping factor means that the amplifier can quickly and precisely return the headphone driver’s diaphragm to its neutral position after each movement, resulting in cleaner and less "boomy" bass.
— Reduced distortion: With a low damping factor, the driver may "overshoot" and introduce distortion, especially in the low-frequency range. A higher damping factor reduces this, leading to a cleaner and more accurate sound.
— More consistent frequency response: The impedance of headphones changes with frequency, and a higher output impedance (low damping factor) can interact with this and distort the sound. A higher damping factor keeps the frequency response more accurate and less affected by this interaction.
— Better dynamic control: A low damping factor can result in the amplifier not having enough control over the driver during fast or loud sections of music. A higher damping factor ensures the headphones can handle dynamic shifts more precisely.

In summary, the 3.5 mm output (0.1 ohms) will give you clearer bass, lower distortion, and overall more accurate sound, especially with low-impedance headphones like yours.

Even though the HIFIMAN HE400se are planar magnetic headphones with stable 32 Ω impedance, they will still be affected by the high output impedance of the 6.3 mm jack (10 Ω).

Still, a lower output impedance gives better driver control, especially for bass. So, the 3.5 mm output (0.1 Ω) will give you tighter, more accurate sound because it provides a much higher damping factor.

As for sensitivity (91dB), it just means the HE400se needs more power to reach a good volume, but it doesn’t alter the importance of output impedance.

I think the 3.5 mm jack will still give you the best sound. Please report back about your experience with this.

I do not want to be impolite, but how can I answer that? Tell me, do you actually have ears? ;-)
How about finding out for yourself?
If you can't hear any difference, then the question is probably superfluous anyway, isn't it?

If you do not hear a difference and are also of the opinion that a higher dampening factor has more impact / priority,
then I think everything important to the topic has been told.

I would understand your question, if there is a reason behind it, that you need to prevent a possibly degraded recording for a paid job. But this is also not the case, we talk in this case about pure listening.

If you are so unsure about the sound, then I can only recommend investing in an ADI-2 DAC FS or even Pro FS.

Then you have everything:
- very low impedance of the headphone output
- enough power
- one Headphone Output (pro: or two of the same kind)
- useful features like auto reflevel, dynamic loudness
- PEQ if you see a certain demand
- a quality which has not to be put in question as you have one kind of output (IEM is a different topic)

We talked already about that

- it is more important to have the bass under control and this doesn't seem to be possible
  with a much lower dampening factor if the information that I got from internet is correct

and that

- the sensitivity only has to do with the volume, whether the headphone output is able to drive your phones.
  in other words: if the bass is under control, which is most important, as you have a lot of energy in the bass part,
  then everything else is also fine

Or do you really think those things that you can't hear has precedence over getting the bass under control?
You have only these two outputs and these two options.

If everything is so critical for you, then take my advice and get the ADI-2 DAC or Pro FS.

With my headphones and I have a few, I can not hear any difference between the 2 outputs too.

Sennheiser Hd600, Mackie hd250, a grado 180, an urbanears, AKG k240 studio, some cheap in ears en others.

Thanks for the comment.
In my case, I was wondering if a 6.3mm output would significantly change the sound of low impedance headphones, around 32Ω, as the output itself has around 10Ω output impedance and is technically made for 80Ω headphones and up, because the impedance of the headphones should be about 8 times up the output impedance of the amplifier.

In your case there shouldn't be a deviation in the frequency response of the headphones as both your pairs of headphones over 80Ω, just the difference should be in the sound level, technically the 6.3mm output is about 3.5 times louder powerful from 3.5mm on headphones with 300Ω headphones.
6.3mm - 35mW at 300Ω
3.5mm - 10mW at 300Ω

It is technically accepted that if an amplifier cannot deliver about 20 mW, it is insufficient for the particular headphones.

Audio Interfaces HP Outputs: https://ibb.co/Czd9FGx