Balanced vs. Non-balanced

I'm not sure but really curious to know what your results are comparing the built in phono preamp with the Parasound. 

Both of your sources will likely yield a 6dB higher output level from their XLR outputs, versus RCA. How any why they do this is another topic. The +6dB is more likely to be useful for analog sources (e.g. to make up for a low-output cartridge) than digital (typically a "hot" output compared to traditional analog sources). 

Does the "common mode rejection" of balanced signal transfer (including AES standard, which your sources are probably not, blah blah) really matter for our typical applications (a few feet / meters of typically shielded cable in a reasonable environment)? Not really. Does the actual RCA vs. XLR input & output circuitry implementation of your components matter? YES, this can impact the sound. You’re right to let your ears guide you here. 

On another practical matter, there are pros and cons to XLR vs. RCA connectors. If you have stiff cables, twisting the XLR pins to line up for connection can be a huge PITA. Some of Audioquest's models will start to separate connector from cable body if you swap cable/components a lot (eventual internal connection fail). RCA plugs can be inserted at any rotation angle, so they're a lot easier to manage. That said, once you line up the XLR pins, you get a nice satisfying lock & click.

@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