Balanced vs. Non-balanced

@mulveling is exactly on the right track here. Likely your turntable with it's inherant lower signal voltage will benefit from XLR (balanced) cabling. Another reason being length, often it is preferable to place a turntable away from speakers, and other sources of vibration, etc. and you can get away using long interconnects with XLR to place a turntable off to the side, on it's own platform, etc. 

OP  I plan on some experimentation, switching back and forth to have my ears guide me.

Human aural memory is fragile. Record the sound when you change different gear. Even better, listen to recorded sounds side-by-side. Upload on youtube and compare. Post the link for everyone.  Alex/Wavetouch audio

Here is Paul's take on this matter:

https://www.youtube.com/watch?v=PzEmKPTb18g

Always go balanced wherever possible.  In this case use the balanced input with whichever source device is more important to you.  Or if not sure try each and decide. Cheers!

So, "listen and decide" is likely the right answer, but I’d also ask "how is balanced achieved in each?".  If they take the unbalanced output and run it through and inverting opamp - fail. Unbalanced will be better. You may be srurprised but this covers the majority of implementations.  If the circuitry is balanced inherently in the previous device, then by all means use it. Unless you have a nonie problem, balanced will have minimal benefit.

I designed some inherently balanced stuff that was produced in high end volumes.  In those balanced was a tiny bit better but only when everything else was done properly.

I should add that the biggest benefit is when there is ground noise.  Done right balanced takes ground noise out of the picture.