Best way to A/B two different streamers

I wouldn't use a switch for several reasons:

1. I keep noticing that the differences between sources and between cables tend to be quite subtle sometimes, albeit still very important. Quick A-B-ing is not the best way to reveal them IME.

2. The logic behind using an A-B switch is something like this: if A>B (A and B are the components to be compared, > means "sound better to me than") then A+X>B+X is also true (where X is the sound impact of the switch and additional cables). This logic is flawed IMO. Just a crude example: say A and B sound very much alike, but A has better treble extension making it preferable. If switch X is rolling off the treble a bit itself, the advantage of A will not be heard anymore through the switch. Another example: A is a bit more refined and detailed, but also a bit boomy and PRAT is lacking compared to B, maybe because the bass of A is more extended and is exciting some room modes more, making it woolly and swallowing dynamics - so I'd definitely prefer B. The switch could reduce and tighten the bass a bit so that A+X (switch) sound more balanced and dynamic, while B+X sounds a bit bass light, thus making me make the wrong choice (A). Of course these are crude and oversimplified examples, but you get the idea.

I think your best bet is to listen to a song through A, than repeat the first 10-12 seconds, then listen to the same song through B, also repeat the first 10-20 seconds and finally listen again through A. I find the A-B-A testing much more revealing than the simpler A-B. This way you will quickly notice the main differences between the sound of A and the sound of B and then confirm and refine your findings through subsequent auditions (other, as different as possible, tracks to listen according to the A-B-A - or B-A-B sometimes, for a change - protocol).

I would not use a switch. Will confound the analysis.

After both are broken in I would try one day one then one day another. Do that a couple times to see if there is some really huge difference. Then I would listen to the music from one for a couple weeks. Then switch, listening for a couple weeks. Do this a couple times and the differences at all levels should become obvious. 
 

If you really want to understand the differences at all levels you have to listen to the music and not the equipment and the differences will unfold.

@ghdprentice - I tend to lean towards this approach.

OP - You should have a sonic memory for the computer, so listen to the new streamer for a few days or weeks and see if you feel that something’s different.  Then go back and verify. If you can’t form an opinion then you’re splitting a hair not worth splitting.

I have found that I have formed an opinion with something new and then when I switched back it was clear that my sonic memory was flawed.  Other times I’ve found it a relief to switch back. Other times the difference was so immediately obvious that I never bothered to go back. 

I just did a shootout like this a few days ago.

1) Connect each to whatever inputs available that both support the source resolution for testing.

2) Stream the same source material with both concurrently

3) Compare. I’d use a sound meter or similar app to make sure both are same volume.

4) Pick the winner and on to round 2 repeating same test but with different input configuration as the challenger if available.

5) Repeat as needed until a winner can be determined from among all the available streaming options at your disposal. 

My recommendation would be to listen to the streamer for at least 3-4 days to get to know its sonic signature. Then switch to your computer as streamer. Spend another 3-4 days if the differences aren’t immediately obvious. Make a playlist specifically for this comparison. Make notes of what you hear. 
If you must use a switch to go between the computer and the streamer, still avoid quickly switching back and forth. Go thru the entire song with computer then the same song in its entirety with the streamer. But…in my opinion using the usb switch can impair the sound quality and you will end up making a mistake…potentially…

FWIW, In every comparison in my system, my mac mini could not match the performance of a dedicated streamer. I used Auralic Aries G1 and Lumin U1 Mini for the comparison (USB cable was Audience AU24se+).