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DAC+ Pro compared to ARcam rDAC

I am currently comparing the Hifiberry DAC+ Pro side-by-side with my old Arcam rDAC. I was hoping I could get rid of the old rDAC, upgrading it to something both better and less expensive. That may seem naive since the rDAC cost about £400 ten years ago (about ten times the current price of the DAC+ Pro) but hopefully not too unrealistic since there the intervening ten years should have seen both technology improvements and price reductions...

I appreciate that this forum is for technical support and you can't and won't comment on subjective taste, but my questions are really about how best to modify the setup of the DAC+ Pro to make the side by side comparison as fair as possible.

For the comparison I have set up two Raspberry Pi 3B systems with the Volumio distro, and connected them as follows:

System #1: DAC+ Pro slotted onto first Pi, output then connected to CD‌ input of my Arcam A85 amplifier.
System #2: second Pi connected via USB to the rDAC, output then connected to DVD input of the A85

(I also tried "System #0": Pi audio jack connected directly to A85 with a 3.5mm to RCA stereo cable. I also tried System #1 into the DVD input and System #2 into the CD input just to be sure the two line inputs on the amp were equivalent - they were. Finally I also tried swapping the RCA audio cables connecting the respective DACs to the amp just to rule that out as a possible cause of difference.)

With the systems thus set up, I can start the same piece of music playing on the two Volumios, and simply flick between the input sources on the A85 amp to immediately hear the output. I am listening through Monitor Audio C180 ceiling speakers - maybe not the most "audiophilist" endpoint, but should be good enough to hear basic differences between the systems!

My observations so far are:
Finding #1 - the rDAC output is a tiny bit louder (I think this may be consistent with published output figures of 2.1Vrms for the rDAC and 2Vrms for the DAC+ Pro?) I noticed this because it was so easy to flick between am input sources, I don't think it would make a difference in actual day-today use. (System #0 is very quiet, which again I think is consistent with Pi jack output at less than 1Vrms?)
Finding #2 - the rDAC sound reproduction is clearer. The DAC+ Pro does a good job (certainly sounds a lot better than System #0), but when listening to the rDAC it's easier to identify individual instruments in a piece of music and the overall experience is more lifelike.

Again, I appreciate that this forum is for technical support not discussion of subjective preferences. I have a feeling that the rDAC's greater clarity *is* objectively measurable somehow but I don't know how. But if we can accept that there is an objective difference (regardless of whether I might subjectively prefer it), my question is what modifications could I make to the DAC+ Pro to make its clarity similar to or better than the rDAC?

I assume the main differences in terms of creating audible differences between the systems are:

(a) the rDAC and DAC+ Pro obviously use different chips (Wolfson 8741 and Burr Brown, respectively). Obviously there is nothing that can be done about this, and if the chips and algorithms etc. used by Arcam are still just "better" in some way then there is no point in tinkering any further with the DAC+ Pro.
(b) the rDAC is in a separate dedicated enclosure with its own power supply, whereas the DAC+ Pro sits on top of, and gets its power from, the Pi. I know that is it possible to tinker with the power supplies here - solder a separate 5V PSU to the DAC+. Is it worth me trying this? My understanding is that tinkering with power supplies are sometimes reported to produce audible improvements, but probably not huge, and perhaps not perceptible on my speakers?
(c) Are there any other relevant differences between the systems, or anything else (perhaps configuration settings in Volumio?) I could try to improve system #2?

Thanks

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