I use an ampsandsound tube headphone amp on occasions when I want that tube sound. Otherwise most of the time I use the ADI-2 FS headphone amp.

On the subject of balanced cabling / balanced operation of headphones, how I assess the matter.

Balanced cabling…

… is absolutely necessary in the studio world or on stages, where you have to deal with higher cable lengths. If you google, up to 100 m seem to be possible. That's significantly more compared to a typical HiFi setup.

The signals are operated at a higher level simply because of the cable lengths. Balanced cabling between devices is a three-wire connection: useful signal in different polarity (+/-) and earth. A differential circuit can eliminate any induced interference by comparing the useful signal in different polarity. Plug shapes: 6.35 mm stereo jack (TRS) or XLR.

For some time now, this form of cabling has been found not only in studio devices or in event technology, but also in consumer devices (hi-fi components). Usually only in the more expensive models as a special quality feature to eliminate possible interference with analogue signal transmission as good as possible, and of course also as a sales argument.

Personally, I also like the XLR plugs very much, they are simply more robust and typically snap into place.

The higher signal level results in a higher listening volume. If you don't pay attention to set volume to the same listening level in A/B comparisons, psychoacoustic effects can give the wrong impression that symmetrical wiring sounds better.

This is because louder sounds better for our perception of sound (ear as receptor and interpretation by our brain). Hence, the loudness war in the music industry, to pay more attention to loudness as well as quality and dynamics in music productions.

Balanced operation of headphones

There is no such differential circuit in headphones.

Here, in my opinion (correct me if I'm wrong) the symmetrical cabling is mainly used to minimize crosstalk between the channels.

Moreover, ADI-2 DAC/Pro (and ADI-2/4 Pro SE) are designed in such a way that in symmetrical operation the signal is completely parallel inside the device, each channel has its amplifier stage. This is then consistently continued with symmetrical cabling / operation of headphones.

But it also has requirements on headphone side that each cable is plugged directly to every driver (L and R) separately.

It has to be said that some headphones (e.g., Audeze LCD-3) have a parallel cable routing from the TRS connector to the speaker due to their design.

The twisted cable will probably also contribute to the cable's immunity to interference (similar to twisted pair Ethernet in the network area).

Especially with headphones like the LCD-3, which has a parallel cable routing practically from the TRS connector, it is questionable whether one can expect really relevant improvements in terms of sound through completely symmetrical operation.

It is only a few millimeters or centimeters from the output stage to the TRS connector inside and regarding the TRS plug itself directly at the unit. At this point in the device and at this short distance, crosstalk, if it occurs at all, is probably extremely low so that it would only be detectable by measurement, but has no significant or audible influence on the sound.

Even with headphones, you have to make sure that the listening volume is the same when A/B testing, so that louder doesn't sound better. With balanced operation, each channel has its headphone amplifier stage.

The higher output power of Balanced Operation can be seen as a useful side effect when driving headphones with extremely high impedance / low driver efficiency. But there were never any problems with the ADI-2 DAC/Pro because the Extreme Power headphone outputs deliver enough power even in unbalanced operation (especially in Hi-Power mode). See also manual chapter 8.1 "Extreme power headphone outputs".

To sum up

Balanced connection of devices and balanced operation of headphones have their technical use cases, but do not expect from it any significant (some people even claimed night/day differences) or the holy grail of better sound.
I hope my explanations brought some light to it.

If you want to use the best of what's technically possible and to be on the "very" safe side, then that's another story, why not. The RME devices support both balanced operation for line inputs and outputs ("with differential circuitry") and also for operation with headphones (essentially for parallel signal routing).

In my opinion, you can't go wrong with the RME devices in terms of quality and features. Not every vendor has a studio background and no other vendor offers this combination of excellent design and quality, driver stability, features and such a great manual from which you can learn a lot.

But whatever I or others say. I propose that you make your own experience. You got now some technical background to digest. Take the time, listen to the devices yourself with your ears, and finally buy what you like most. You must feel comfortable with your purchase decision and the device.

If you want to try out other sound signatures get some other phones. Another transistor amp chained to ADI-2 DAC would be useless and waste of money. Some forums will tell you to get three versions of chinese amps, but its bullshit. As a previous owner of ADI-2 DAC and now PRO, balanced is only needed if you have phones with certain needs for high power. It doesnt sound better, more balanced or even differnt. Only if your headphones need that kind of output to perform.

If you purchased the ADI-2 DAC you are right there you should be, excellent desicion!