Just for fun, I made a couple of measurements comparing headphone frequency response versus DAC/amp for my M2U&M2U stack and my Benchmark DAC1USB, using Beyerdynamic DT770Pro, DT880Pro, and Sennheiser HD650 headphones. The results show that the DAC/amps are remarkably similar in overall frequency response.
I used an Earthworks M23 microphone as my measurement microphone, connected to a Roland OctaCapture and my Laptop running SMAART software. I made a mic & headphone holder to ensure consistent placement and [not-so-accurately] simulate a head wearing the headphones (I forgot to take a photo... I'll try to add one later). The software generates broadband pink noise which was fed to each DAC via the coax S/PDIF connection running at 24 bit 48 kHz. I used a calibrated sound level calibrator to calibrate (that's a lot of "calibration") the levels measured by the M23 microphone, and then adjusted the output volume of each amp until the software saw an 80.0±0.1 dB pink noise signal. I did not touch the headphone between measurements on each DAC/amp to ensure maximum consistency. I selected a 5-second average for the transfer function measurement and let it run for about 15 seconds before capturing the response curve. I did not apply any smoothing. Signal delays were accounted for and zeroed out in the software, which is evident in the phase plots (not included in this post yet). I did notice that the signal one DAC was delayed by ~1.25ms more than the other (I think the DAC1 had the longer delay... will have to check my raw files later). This latency has no impact on listening to music. On my last measurement with the HD650s, I also measured the M2U setup in both low and high gain settings.
Here is all the data in one plot with a ±10dB vertical scale. Overall, the curves for each headphone are remarkably similar regardless of DAC/amp used. There is nothing here that would suggest spectral differences in the sound signatures, which agrees with my listening--I cannot tell any real differences between DAC/amps.
Here is the DT770Pro by itself through the M2U and DAC1:
Here is the DT880Pro by itself through the M2U and DAC1:
Here is the HD650 by itself through the M2U and DAC1:
I plan to repeat this test again when I have a little more time. I think that my test environment was not ideal as there were a few background noises in my house at the time. A repetition will tell my how accurate my calibration and headphone-to-microphone placement was.