Yes, it is a combo but depending on what headphones you are going to drive, you may need more power. You can read my review on it here for more details:
Better is very subjective once you get out of DACs/Amps that don’t perform well and into decent ones.
And while I do agree that the headphones will make most difference, certain headphones do work better with certain amplifiers.
I am not sure what comparisons you are referring to but the HD6 series is generally regarded higher than the HD5 series.
However, they are headphones that scale well and do need a certain amount of power, so if the comparison was done on something like a smartphone, PC headphone jack etc. then it is possible that the HD560 performed better.