Thanks for the information. My reasoning here is that the M11 has all three of 2.5/4.4mm(?) balanced, and 3.5 unbalanced outputs, and my possibly flawed understanding is that its dual dacs provide more power to the outputs...
A DAC is a Digital to Analogue Converter. It doesn't provide power. The closest thing to a DAC providing power is an integrated audio chip designed with the DAC chip and an output stage that kind of approximates what an actual discrete output stage does, but then you'd still be limited to a 7.2V battery shared with a CPU and screen.
Think of it like an AMD APU in a Sleekbook vs a CPU with a discrete GPU on a desktop or those new flagship laptops that need two powerbricks just so the desktop-grade i7 CPU and xx80 GPU will run.
What having separate DAC chips does depending on each chip design is whether it can simplify designing a balanced drive circuit. You can still have balanced drive and high output from a single DAC chip depending on the output from it, but most of the time it has less to do with how the chip works and more with "nah let's keep each channel completely separate" which works better in marketing ie how people will choose that product for being made that way rather than hearing the difference between just having two DACs whether the amp stage is balanced drive or single ended.
In this case what drives your headphones are two OPA926 op-amps.
I may be wrong on all counts, but as I am trying to buy a headphone to match the device, and all the premium IEM's for FiiO sell are dual inputs, I wanted to understand it and know what my options were. The M11 is the source of all my dac and amplification. (I'd prefer not to have a separate headphone amp as well, most of the time it shouldn't be needed for the M11).
Think of it this way.
Putting balanced drive on the DAP that has to work off a small battery and using it with a high impedance headphone or a low sensitivity headphone is kind of like putting a turbo on a 2.0L inline 4. Sure it'll run a midsize car like a BMW 5series or similar a lot better than the naturally aspirated version on the 5series that took you from the airport to your hotel, but don't expect that it's going to be closer to an M5 with a V10.
For a 300ohm 97dB/1mW headphone, if you really want eitehr to sound "alive," you'll need at least around 128mW, preferably 256mW. That player has 88W at 300ohms balanced.
That said if you used a newer design, low impedance, high sensitivity headphone, its 225mW at 16ohms, 195mW at 32ohms can already be overkill quantity-wise, enough that a desktop amp's only real advantage is you don't have to charge it or you get lower distortion and noise from a good Class A desktop amp. A Grado at 32ohms, 99dB/1mW only needs around 64mW to 128mW. The HiFiMan HE400S at 22ohms, 97dB/1mW needs 128mW minimum, preferably 256mW (same as the 300ohm headphone above, but has a lower impedance, and so gets that much more power out of the player). And these are single ended output figures, no balanced drive.
In sum, I'd use this player with my HD600 if my amp is busted, but I wouldn't buy the HD600 specifically to use with it. I'd use it with Grados and not blow any money modifying the cables though and you might as well just spend on an RS1e than for example an SR325 with balanced cable mod. I'd get the HE400S and if it's that cheap and all I need is to swap a cable, I'd get a cheap cable to run balanced drive on it.