OK ... I previously reported in this thread that my Bass Chorus Deluxe was completely issue/hiss free, but now that's I've tried it with headphones, I can 100% hear what you're talking about. Using the headphone jack on my GK MB115, everything is perfectly silent so I can really hear what should and shouldn't be there.
I will admit I need the headphones on to hear it ... a hiss, or to my ears it's more like a faint rattle (like the springs of a snare drum rattling. Very faint but audible nonetheless). It is present when a note is being played, and the noise sustains as long as the note does. I start to hear it with the treble at noon, and it becomes more noticeable with any increase beyond that (I prefer having the treble at about 75% full).
It's definitely there and I think it most definitely impacts the tone. My tones from my MXR Phase 90 and Carbon Copy for example are deep and full and clear. I like the tone of my Bass Chorus Deluxe, but it doesn't have the deep/full/clear tone I've experienced with other chorus pedals and other MXR pedals. Switching from another pedal to the Bass Chorus Deluxe, or from bypass to the Bass Chorus Deluxe, I would say some of the clarity is being sacrificed. Though you wouldn't necessarily hear the rattle/hiss, the fact it is there impacts the the end result of what you do hear.
As the honeymoon period wears off, I do regret selling my MXR Black Label Chorus before I even received the Bass Chorus Deluxe. I loved the Black Label Chorus and assumed the Bass Chorus Deluxe had to be just as good and would most likely be better. The main reason I replaced the Black Label though was I was really attracted to the flanger function of the Bass Chorus Deluxe (and I really do like the flanger in this thing).
As for the straight chorus tome, I remember INSTANTLY being wowed by the Black Label Chorus when I first got it. Plug it in and wow. Just two days ago a purchased a MXR Phased 90 ... again INSTANT wow. I also own the MXR Bass Envelope Filter, MXR Bass Compressor, MXR Carbon Copy, MXR Bass D.I. ... all wow wow wow wow. With the Bass Chorus Deluxe, it's been more like, "ok, the more I play it, the more I'm liking it, I'm learning to love it ... I have to love it because it's MXR ..."
Would I have noticed the noise at all if not for this thread? No. But again, there was "something" that was making me miss the tone of the Black Label Chorus and that little sound in the Bass Chorus Deluxe, as faint as it is, is likely interfering just enough to alter the overall tone.
Anyway ... I'm keeping it. I still like it much more than my previous EBS MultiChorus. The faint noise doesn't bother me enough to ditch it.
With that said, I think it's still a legitimate issue that is getting in the way of the best tone possible. It's good, very good ... but it can be better. If I hadn't already bought it, I wouldn't have got rid of my Black Label and maybe waited to read all the feedback from the first shipment of pedals that went to market.
In a nutshell ... not disappointed, not "wowed" by it either ... but I'm OK with it.

If it wasn't for all my previous happiness with MXR/Dunlop, I may not be as laid back about it (including Way Huge, 7 of the 9 pedals on my board are Dunlop/MXR).