The C-2v and C-s ground and low-lying states of doublet CuO2 are examined for a series of different density functionals (pure, hybrid, and meta-hybrid) and CCSD(T) methods. The effect of changing the B3LYP functional a(0) parameter is also explored. CCSD(T) results at the complete basis set limit show that the relative stability of the different electronic states is (2)A(2)(C-2v) < (2)A ''(C-s) < B-2(2)(C-2v) < (2)A'(C-s) << (2)A(1)(C-2v) < B-2(1)(C-2v). Unlike CCSD(T), all DFT methods analyzed in this work erroneously predict the end-on (2)A '' state as the ground state for CuO2 irrespective of the type of functional and percentage of Hartree-Fock (exact) exchange included in the B3LYP-like functional. Among the different functionals tested, B3LYP gives the best geometries and relative energies for the different electronic states when compared to CCSD(T) results. As for the effect of the a(0) parameter, it is found that the B3LYP-like functional yielding better geometries contains 20% of exact exchange, although somewhat unexpectedly, the B3LYP-like functional with a larger contribution of exact exchange (90%) is the one that gives the smaller standard deviation for relative energies.