>Other than ancient compatibility purposes...

That's actually not true. That plug is commonplace on a lot of music equipment, DJ mixers, etc. that are still manufactured and used commonly today.

Sorry, I wasn’t very clear. I simply meant the standard has been around forever, not that it was obsolete.

I figure there has to be some reason for it in an age when companies are constantly cutting costs.

6.35 mm jacks are quite a lot more robust than their smaller 3.5 mm brethren.

Which can be a problem when you plug them into the phone - you probably don't want your plug to be more robust than the socket.

you might if your headphones are worth more than your phone ;)

I doubt many people are trying to drive HD-650's with a phone anyway.

I don't think it's about ancient compatibility but rather just the fact that audiophile stuff tends to have it and if you are marketing to audiophiles, might as well design it that way. I have a pretty modern stereo receiver (Onkyo A-9010) as my computer's headphone amplifier and it has the bigger socket only. Same with my home theatre receiver (also an Onkyo).

But I believe there's no difference in listening experience. The bigger plug is probably a lot sturdier though. I've had some 3.5 mm jacks bend on me. Can't imagine that on the good ol' 6.3. I have totally busted a 6.3 mm to 3.5 mm adaptor though.

As others have stated, it's usually more about compatability. Most (nonportable) headphone amps will have a 1/4" plug rather than the 3.5mm, and it makes more sense from the "female" amp side to convert the larger 1/4" --> 3.5mm than the other way around. Many home "audiophile" headphones I've used (Audeze or Beyerdynamic) actually have the smaller 3.5mm jack, but because they are so focused on home use (bulky, open backed, expensive, and not very shovable into a backpack), users rarely use them connected to a phone or laptop.

There is no signal or quality difference between different sizes of headphone jacks, except that bigger ones might last longer.

For very long cables or high RF you might want a kind of cable called "balanced", which comes in every size except 3.5mm. Some audiophiles think these make headphones sound better, but it's probably not true.

its standard in audio. all mixers, guitar amps etc support them. big plug means stable wide signal, and it does not break. never had one break ever. even the shitty cables. they are well shielded.