I own the CS-600, the integrated big brother to the CS300XS, so I'm not sure a comparison between that piece of kit and the EAR are what you are really interested in. From what I've read on this thread, the 300XS plays nice with a wide variety of headphones, as does the 600 (except for the low level hum it exhibits with higher sensitivity headphones) as does the HP4 but without any hum, although I rarely listen to cans through the Leben. If I were to choose one of the two for headphone use only, it would be a no brainer. Purchase the EAR and roll the tubes with your favorite vintage flavor. Unfortunately though, the HP4 and Orthos really don't mate well while you could do a lot worse listening to Audezes or HiFi Mans with the Leben (low sensitivity = no hum)
My favorite headphone is the HE-6, which I listen to through a linestage and a 55W tubed power amp connecting to the speaker taps of the amp to power the cans. I pair the LCD-3 with an SS Bakoon Amp 11-R, a virtually unknown integrated here on Head Fi but a meticulously designed component on the same level as amps designed by Nelson Pass. Last, but certainly not least, I only listen to the EAR when in the mood for the AT W3000ANV. I don't believe the HD-800 would be my cup of tea so I don't own a pair. Never owned any Stax gear and don't feel the need to go that route.
My goal is to create the "magic" by marrying the headphone to the amp on hand that has the best synergy. The three combinations listed in the above paragraph do it for me. Personally, I would not purchase a Leben integrated for headphone use only. The odds are too high that the high sensitivity cans in ones collection will be subject to the dreaded hum.