Hello Kata.
I have never owned ESL63's, but used ESL57's for years. (Still have two pairs.) So no direct experience - treat my reply accordingly.
I understand that the ESL63's are very similar to the latest 2x05's. The main differences are build quality and rigidity - newer being better. I found my unmodified 2805's to be punishing with a digital source - any music at all - but worse with recordings which used distortion as a design element. After modification this improved, but vinyl was still far superior.
To my ears, the unmodified 2905's seemed more forgiving of digital distortion, but still too revealing for comfortable listening. After modification this effect diminished - it was as if some edge detectors had been removed - as indeed, an electrolytic cap had been removed. My solution is to put a 13KHz filter (6 dB per octave) between the player and the amp. Since I built my own pre-amp, this was easy, and very worthwhile.
A very much cheaper solution for digititis is to stack several ESL57's. I find my stacked ESL57's just as musical and satisfying as the modified 2x05's - but lacking the high and low octaves, and some mid-range clarity. Stacked 57's offer very good value for the money, and they pair quite well with the B3-SST Brystons (I would guess the newer Brystons are even better), which are bullet-proof.
Stacked ESL57's, with all their limitations, are more musical to my ears than any other brands I have heard, including Magnepans and Martin Logan hybrids, which I also own.
My suggestion: for analog, modified 2905's. For digital, modified 2905's plus a filter, or stacked ESL57's.
Hope this helps - but remember, just one geek's opinion.