Balanced Inputs

If your DAC is fully balanced in and out (2 DAC chips per channel) the XLR output should perform better than its RCA output summing circuit. Otherwise you're probably better off with the phono.

Balanced inputs often offer 6dB increased gain. That can be valuable for a phono, worthless for a DAC

6bB less gain.

Tiny amounts of gain can be lost with very long interconnects. So do keep that in mind.

Really it is zero.

If two pieces have XLRs it gets to be a coin toss.
I run the DAC into mine.

I don't think any of my gear is truely balanced.  I have a modest system:

Technics SL-100C turntable

Ortofon 2M Black cartridge

Denafrips Ares II DAC

Audiolabs 6000CDT transport

Parasound Zphono XRM

Parasound Halo P6 preamp

Parasound Halo A23+ power amp

Does the implementation of your XLR input use a jensen transformer?

The Denafrips Aries II is stated to be truly balanced.

I have mine (Aries II) going from its balanced outputs and into the balanced inputs of my Belles Aria Signature pre.

If I had to choose between the DAC and phono, I would probably go with the DAC.