I'm a bit of a delay junkie. They both sound great. I've had the regular CC and the DTjr. The DTjr has the tone control going for it which makes it quite flexible; the CC has a really nice mod obvi. If I had to pick one I would have gone with the CC, but I just prefer analog delays.
As far as simple analog delays go, I LOVE my Moog mf-delay. It just sounds so thick and I like the way it sits in the mix. I'd say it's a darker sounding delay, though brighter than the CC. The Moog seems brighter at lower delay times than higher, so you can get an excellent slap-back, then crank up the time for a more moody atmospheric kinda thing. The Boss Dm-2 and the EHX Memory Toy also sound great in my opinion; if you happen to try it out, keep in mind the Memory Toy's modulation is internally adjustable. I haven't played one, but the Seymour Duncan Vapor Trail sounds great in the demo's I've heard.
In the digital department is the MP Deep Blue Delay; it's digital, but it's not definitely not pristine, and has a bit of a noisy analog flavour, though it's much brighter. And just in terms of sheer versatility and sound quality, there's Boss DD-7 and the EQD Dispatch Master.
I was always a big analog delay guy. These days, I find digital has surpassed analog, for analog delay!
Analog delays are a bit too choppy for me and analog sounding digital, to me, is smoother, thicker, and more versatile, plus I find it better for ambience. I don't use tap tempo nor care if my delay is in time, because I use delay for space, wetness and ambience. It be the compander I do not like.
My Digitech Obscura beats out all of the analog delays I have owned.
The Dispatch Master didn't work for me, although sounded incredible. In my amp loops, it had a noticable volume drop so I reluctantly sold it. I also prefer faux echo created with delay, than actual reverb.
I really want to get the E.D. Disaster Transport. On paper and from demos, it sounds like my dream delay. Amazing delay, tone knob. Modulation and a footswitch for the modulation.
I had the Moog MF delay but I didn't like how it was voiced and to me, it always sounded too slap back like and had some reverb like qualities I didn't like.