Hey Vka! I see you finally acquired the SCD-1. Man isn't it a beautiful unit eh? Not to mention all those shiny metal used in the construction weights a ton. That's the only thing I hate of high-end suff. It seems that as you climb up the ladder, the toys seem to get heavy and heavier.
Balanced connections are not popular with headphone system. I believe this is due to the fact that many amps are not made with balanced inputs (even your mighty DCT-1 unit). Hence, not much response to your question. You probably remember I once owned the 777ES Sacd Player (essentially the same to the SCD-1, but without balanced inputs). I replaced it with the Electrocompaniet EMC-1 unit. Using the balanced outputs of EMC-1, I get some extra headroom on my tube amp. Where I recall using unbalanced inputs on the Sacd Player and the unit I have now, my maximum listening volume top off around 5 1/2 no more than 6 depending on the quality of the recording. Using balanced via the EMC-1 unit, my maximum listening volume is around 5 (of course, 10 is the max on the volume pot). I suspect the voltage of the balanced ouputs are far greater than unbalanced ones. Check the spec on your unit to see if this square with my findings.
As far as the music is concern, I have to agree with DanG. While I don't claim to hear any differences between the two, balanced configuration is definitely quieter. When you get a chance to listen to the balanced ouputs of your SCD-1 unit, pay close attention to the noise floor (this is where you'll hear the biggest differences). A quiet noise floor allow you to hear the fine detail otherwise mask over.
I've talked via e-mail with one of the fellow who I believe is a die-hard enthusiast in this hobby. When I inquire the same query, this is what he has to say:
"I got into the stereo arena about 1.5 years ago and upon starting I checked out the difference between RCA and XLR ends. At the time, I discovered that balanced was a quieter method of transferring a signal between two points. This is a fact and not conjecture. Since then, a number of amplifier manufactures have gone to only balanced inputs (i.e. Pass, Mark Levinson, etc.). Transparent will be the first to tell you that the Transparent Reference XL balanced is almost 6db quieter than the RCA ended interconnect. I feel that more and more you will see balanced take over the high-end market, especially here in America. The Europeans, however, just do not want to switch.
Regarding your friends saying balanced is no different than RCA I would propose the following: first is that they have not gone to balanced throughout their system and/or have a "weak link" somewhere along the way (i.e. an RCA connection or something of less quality within the system); second is that the system they have is not of high enough quality to reflect the difference (i.e higher quality the system the more of a difference it makes). If you will notice on audiogon.com you will see how many of the high end RCAs are being sold. I would propose that this is being done because those with the high-end systems are going to balanced.
Finally, I would suggest that you contact Pass Labs or Transparent Audio and have one of their technicians describe why balanced is the way to go. Not trying to be "snippy," just trying to inform."