I personally could not hear a difference balanced vs SE on 600i, nor the GSX MK2.
The only one that I may possibly heard some differences would be the Bryston BHA-1. Certain headphones like the more hard to drive is worth using balanced on it, but it puts out so much power balanced that, it's not worth it with lots of headphones. Channel balance is much greater importance than having to use balanced.
You'd have to level match to know for sure. Balanced to SE switching, you are going to much greater power balanced, and people are not going to properly level match for comparisons.
Due to our ear sensitivities varying across the spectrum, at louder volumes, we hear more bass. This is why level matched is important for more accurate comparisons or it's just another impression.
So, there are a few underlying things people should take into consideration than just take for face value. For example, you do a placebo test on subjects with balanced connection outputting identically to SE.