We previously introduced [T. Cren et al., Europhys. Lett. 52, 203 (2000)] an energy-dependant gap function, $\Delta(E)$, that fits the unusual shape of the quasiparticle (QP) spectrum for both BiSrCaCuO and YBaCuO. A simple anti-resonance in $\Delta(E)$ accounts for the pronounced QP peaks in the density of states, at an energy $\Delta_p$, and the dip feature at a higher energy, $E_{dip}$. Here we go a step further : our gap function is consistent with the ($T, p$) phase diagram, where $p$ is the carrier density. For large QP energies ($E >> \Delta_p$), the total spectral gap is $\Delta(E) \simeq \Delta_p + \Delta_\phi$, where $\Delta_\phi$ is tied to the condensation energy. From the available data, a simple $p$-dependance of $\Delta_p$ and $\Delta_\phi$ is found, in particular $\Delta_\phi(p) \simeq 2.3 k_B T_c(p)$. These two distinct energy scales of the superconducting state are interpreted by comparing with the normal and pseudogap states. The various forms of the QP density of states, as well as the spectral function $A(k,E)$, are discussed.