So first some details (in my country)
HD559 = 70$
HD599 = 144$
HD560s = 240$
HD559 are the only Sennheiser that i don't quite like (bloated,muddy,etc).
From 559 -> 560s is an insane jump (also 3x+ the price) but i feel its worth it (in my opinion of course).
With 559 you can only listen to EDM, Rap, Trace (bassy songs) and maybe something with vocals but bass bleeds into mids.
They suck with games, movies, youtube, etc. So i can't really recommend them.
Bass goes deep (on some songs it rattles), has speed and feels overall just better.
So 560s are the best in the 5xx range. I like them over the 6xx aswell but 6xx has it's place.
If money were no problem i would own: 599, 560s and 6xx for sure.
Maybe i'll go for the 660s in the near future.
Hope this helps, im here if you have more questions. Again, my gear is in my sig, also my spotify playlist.
Im also aware that the DAC im using its not the best. I'll get a Topping D10s or something better next month.