Since this thread is allegedly about our opinion, here is mine (experience based). I’m an objectivist, measuring everything I can to confirm that equipment is in the good technical quality range. Careful subjective evaluation is next.
Based on all my knowledge, I expected that two DACs having the same SINAD of >120 dB, and using exactly the same ESS chip (Topping E50 and Gustard x16), would sound indistinguishable. Alas, bad news for my wallet.
After accidentally burning out USB port on Topping, I ordered Gustard x16, which arrived the next day. Listening first song made me surprised. Treble was not higher in volume but was more pronounced and clear. Multiple voices separation was better and I could easier understand lyrics. There were other small differences. There was absolutely no expectation bias on my side.
So, yes, two simple measurements like distortion and noise, although both values are orders of magnitude below believed thresholds of hearing, are not enough to determine that equipment will sound the same.
Based on all my knowledge, I expected that two DACs having the same SINAD of >120 dB, and using exactly the same ESS chip (Topping E50 and Gustard x16), would sound indistinguishable. Alas, bad news for my wallet.
After accidentally burning out USB port on Topping, I ordered Gustard x16, which arrived the next day. Listening first song made me surprised. Treble was not higher in volume but was more pronounced and clear. Multiple voices separation was better and I could easier understand lyrics. There were other small differences. There was absolutely no expectation bias on my side.
So, yes, two simple measurements like distortion and noise, although both values are orders of magnitude below believed thresholds of hearing, are not enough to determine that equipment will sound the same.
I would not attach too much importance to measurements. I especially wouldn't base my decision on what equipment to get. They are necessary to determine whether the device works as intended, that there are no problems and the like, but that's the end of it. Subjective feeling is certainly more important, good measurements are useless if it sounds boring, which often happens.
To measure ITD phase coherence between channels would require finding a test that correlates with human hearing of music in trained listeners on a qualified system. Its probably something like looking for a phase difference of a small signal, say at -60dB when both channels of the dac are playing different music or different 20-tone test signals. Is there any phase difference for the -60dB test signal between channels, including difference in phase noise? Same thing if the 20-tone test signal is turned on and off rapidly. Is there any phase noise or phase shift change in the -60dB test tone?
According to several studies the threshold minimum for ITD is about 10us at 1000Hz (for sine signals). Threshold is higher at low frequencies and for complex music the threshold is probably even higher. This 10us time difference would mean about 1 sample difference at 96kHz and 7 sample difference at 768kHz. Do you have any evidence that some well measuring DAC would have such timing differences between channels? And what would be causing such time difference?
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3663869/
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3663869/
Benchmark DAC-3 was different from Topping D90. DAC-3 sound stage was narrow and forward, mostly out in front of the speakers (IME a sign of a type of random noise jitter problem).
OTOH, D90 at bass frequencies was very wide extending horizontally somewhat wider than the speakers. At higher frequencies it sounded more like the sound was coming out from the speakers rather than between and extending behind them. Also there was something not quite right with sound at vocal frequencies and higher (such as for cymbals). The unpleasant effect got worse as frequency increased.
Regarding well measuring dacs, if there was a difference in phase noise of a low level signal, it could depend on the other signals present at the same time, especially if they are changing dynamically. Test tone phase noise could also change due to substrate coupled noise from music playing in the other channel.
Whether or not steady state (PSS) type testing would show a steady state difference is harder to say.
OTOH, D90 at bass frequencies was very wide extending horizontally somewhat wider than the speakers. At higher frequencies it sounded more like the sound was coming out from the speakers rather than between and extending behind them. Also there was something not quite right with sound at vocal frequencies and higher (such as for cymbals). The unpleasant effect got worse as frequency increased.
Regarding well measuring dacs, if there was a difference in phase noise of a low level signal, it could depend on the other signals present at the same time, especially if they are changing dynamically. Test tone phase noise could also change due to substrate coupled noise from music playing in the other channel.
Whether or not steady state (PSS) type testing would show a steady state difference is harder to say.
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I like buying the most expensive equipment regardless. At least I can tell someone how much it was. I never demonstrate anything in case the listener says something bad and I have to kill him 😡 
There are some subjectively evaluated measurements at: https://www.diyaudio.com/community/threads/phase-noise-in-ds-dacs.387862/post-7063038
Yes, that thread has such measurements. DAC and ADC should be synchronized for that type of measurement. The noise skirts contain both phase modulated noise (mainly from clocks) and amplitude modulated noise (mainly from Vref). So that type of measurement is not well suited for measuring clock phase noise only.
Just as an example of lousy close-in phase noise in chifi dac here is >120dB SINAD SMSL DO300EX with AK4499 (in green) compared to Diyinhk AK4490 (in blue), (courtesy of @gaycoh).
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The original question was: "can DACs sound different if they both measure well?" Nothing about the differences being huge or small. Besides, I was under the impression that the question relates to things that are usually measured rather than things that could be measured, but that was just my interpretation.
No idea.
What I do know, is that many things audiophiles seem to like have the side effect that they reduce intersample overshoot issues:
Very high sample rates
Non-oversampling DACs
Raw-DSD DACs
Possibly apodizing filters
I know one big counterexample: the tendency not to use digital volume control.
If we are talking about Dac chips alone then I'm in the camp that if they measure the same then they will sound the same.
If we are talking about whole implementations from input through to analogue out, then it's cloudier.
I'd still say that the implementation of the Dac chip is as important as the thing itself.
The swankiest Dac chips can be made to sound so-so.
Cheaper value ones, well implemented, can sound right up there.
See, I wrote all that and still stayed on the fence - sort of😂
If we are talking about whole implementations from input through to analogue out, then it's cloudier.
I'd still say that the implementation of the Dac chip is as important as the thing itself.
The swankiest Dac chips can be made to sound so-so.
Cheaper value ones, well implemented, can sound right up there.
See, I wrote all that and still stayed on the fence - sort of😂
Measurements not equal sound. Differenent DAC chips has its own sound signature
But DACs are typically measured from the analogue outputs. So if they measure as audibly transparent how can they sound different? It does not make sense for them to sound different. If distortion is well below audible how on earth can the signals be audibly different? The only way that is possible is if the distortion is causing the signal to change audibly which means the distortion would be much higher.
By the way, I posted some test signals that make clipping on intersample overs very audible here:
https://www.diyaudio.com/community/attachments/intersample-zip.1061539/
https://www.diyaudio.com/community/attachments/intersample-zip.1061539/
Steady state distortion looks like a spur on a FFT, right? What that means is that the distortion signal energy is concentrated in one bin. However, it common to spread out distortion across multiple bins to make it look more like noise on an FFT. Only Cargo Cult Science professes that there are only steady-state distortion spurs and nothing else.
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