Balanced sounds better because it has better channel separation (less crosstalk), than single end, on most DAPs. It's not about the power. Greater channel separation means better stereo imaging, as well as better (accurate) sound stage. There is a russian site called "
https://reference-audio-analyzer.pro", that has very detailed measurements of different DAPs (some are still missing, like Hiby's DAPs, but I hope they will expand).
For the Fiio X7 MarkII, here are the measurements for the unbalanced output (which is kinda bad):
Link
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and here are the measurements of the balanced output (which are not the best compared to some other DAPs, but still decent, especially compared to the single end):
Link
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The ideal channel separation (just like the noise floor - SNR) for CD quality (16/44.1) would be at least ~95,6 dB (the higher the number, the better). The threshold at which sound turns into mono (or completely washed out, in terms of imaging and soundstage) is at 40dB, and everything below is... well... pretty much mono crap. You can also see, that crosstalk is different (especially for the single end output) for IEMs with different impedances (lower impedance means more crosstalk, which is kinda strange, but... it is what it is, probably because of the internal impedance of the DAP, as well as some other factors)
This is more of a tip for those that are looking to buy a DAP (or taking the best out of their existing DAPs), but still I think it's important to note. It's not about power, it's about probably the most important SQ feature - stereo imaging. As I've said in the past, most DAPs are only worth it for their balanced output, because even some phones beat their single-ends, which is kinda sad.