The MXR is the best delay sound I've used, but the DD3 has 2 advantages for me.
Firstly, it's easy to adjust on the fly. I use 3 delay settings, and not having room on my board for a bigger unit, I can twiddle between songs quickly with the DD3; near enough is good enough on it's controls, it having the delay time switch. The carbon Copy OTOH is quite sensitive, having a lot of range on it's controls, so you can end up a long way from your ideal sound with only a small control deviation.
Secondly, even though the MXR CC has a lovely clear, but warm, sound, you need (IMO) digital clarity to cut through with long delays/several repeats in a live context. As my base sound is already vintagey warm, with not expecially clean cleans, the digitalness is ok for me, and the way it cuts through suits me better.
Otherwise, for instance, I lose the last few repeats in the mix.
Other people's set ups and requirements will vary, and If I only used one delay sound, or only needed shorter delays I would prefer the MXR.
Hope this helps. :)
