Holy moly there are some fundamental misunderstandings here!
OK, so you guys remember that V*A=W, right? Good.
And you remember Ohm’s law? OK.
So, for a given headphone, its maximum wattage is some combination of a voltage and a current. The impedance of the headphones dictate whether it prefers a higher voltage and lower current (high impedance headphones), or lower voltage and higher current (low impedance headphones).
Portable devices generally have quite low voltage limits, but the batteries can provide significant current, so low impedance headphones do better here. Typical values are between 16-40Ω. This gives good volume even on portable devices.
Mains-powered amps generally have much higher voltage dual-rail power supplies, and thus can do much larger voltage swings, supporting high impedance headphones. Some divert a pair of speaker amps to the headphone output via relays, others simply use a separate op-amp headphone amp.
A speaker amp intended for speakers won’t have any trouble with headphone impedances far higher than the speaker impedance, simply because the maximum voltages needed for loud playback on speakers is far higher than needed for headphones. The current involved is negligible compared to loudspeakers.
So, with those fundamentals out of the way:
For something like a personal music player the 400 ohm devices will be best as they will present the highest possible load impedance to amplifiers that are meant to drive headphones anyway. When listening to a HiFi amplifier the 16 ohm devices will be better as they are closest to the impedance of the speakers, although there may also be series resistors in the amp to reduce the level.
That’s absolutely, 180˚ backwards. Portable devices like low impedance headphones. 400Ω aren’t going to be very loud at all on a portable device. 16-40Ω is the typical range.
The impedance is 400 Ohms according to this spec sheet which I found by googling for Beyer Dynamic Dt 100.
https://north-america.beyerdynamic.com/amfile/file/download/file_id/4831/product_id/1478/
This is a much lower impedance than typical headphones for MP3 players and the like.
Recording studios often run on lower impedance. Apparently (as provided in the spec sheet) there is another version, the DT 102 which runs on 16 ohms which is closer to some loud speakers.
No, that is far, far
higher than typical headphones for portable devices.
It’s studios and audiophiles that tend to run high impedance headphones. (I have yet to come across a convincing explanation of why high impedance headphones are supposed to sound better than low impedance ones, but it’s a common belief.)
In ear earphones/earbuds are usually very sensitive at any impedance level, far more so then on ear headphones, which is a problem since the EU started mandating maximum levels for consumer gear based on the assumption that we were all using the nasty things.
Just a little niggle: headphones, earbuds, and in-ear monitors (aka in-ear earbuds) are
three different kinds of earphones, not two. The volume characteristics of in-ear types are very different, since they significantly block outside noise by sealing off the ear canal, reducing the amount of volume needed compared to earbuds that do not seal off the ear canal. And I categorically disagree with you dismissing them all as “nasty things”. There are some very, very, very nice in-ear earbuds out there.
The EU limit is a bad design, IMHO, since it’s based on “maximum volume with the pack-in earphones”. So the second you plug in some other model of earphone, the maximum volume may be too high or too low. So dumb if you ask me... (Never mind that higher gain may be needed to boost quiet content...)