Which IC is more important?

I don't know if this has been addressed specifically before, but I couldn't find it searching thru the cables forum. At the risk of being redundant, I'll put this forward to the community.

Looking at a CDP - line stage - amp sequence, which of the two IC's is more critical? Any reason, scientific or other, as to why? What have your experiences been in using different IC's in these places (ie. type of IC, quality, cost, etc.)?

Looking forward to hearing about your experiences.