Balanced inputs often offer 6dB increased gain.
This is only true if the equipment supports the balanced standard. Otherwise the gain does not change.
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
Almost all phono cartridges are balanced sources and most tonearms (including all Technics arms I've seen) are too. Your Parasound treats the balanced source as single-ended however. But it does have balanced outputs...
So I would put this down to which source you want better fidelity since the balanced connection usually offers better sound quality.