When is it better to use coupled-cluster (CC) over configuration interaction (CI) calculations?
CCSD is preferred in nearly all cases because size-extensivity/size-consistency is a critical property to have for practical chemistry, and on top of that, more of the correlation energy (the part of the energy missing from Hartree-Fock) is captured by CCSD. CISD only accounts correlation energy for up to double excitations and not at all for higher excitations. CCSD accounts for correlation up to double excitations and then approximates all higher excitations as combinations of the single and double excitations it has already calculated. This gives much more accurate numbers for pretty much all systems and provides for size-extensivity/size-consistency. The only time you would really be better off doing CISD than CCSD is if you wanted to do full CI on a 2-electron system, in which case CCSD is not as efficient.

So in short, CCSD is preferred because it almost always gives better, more usable numbers than CISD for similar or better costs (they both scale as ~$n^6$).