The single-mode regime of 19-cell Yb-doped double-cladding photonic crystal fibers, successfully exploited for high-power applications due to their large mode area, has been studied. The first higher-order mode cut-off wavelength has been evaluated taking into account the crossing between its dispersion curve, obtained with a full-vector modal solver based on the finite element method, and the one of the fundamental space-filling mode, calculated for an infinite cladding. Moreover, the overlap integral on the doped core of the higher-order mode at cut-off condition has been calculated, in order to investigate its effective suppression in the gain competition with the fundamental mode, by applying a spatial and spectral amplifier model. 19-cell double-cladding photonic crystal fibers with different core diameter and refractive index values have been considered. Simulation results have shown that the approach based on the fundamental space-filling mode effective index is not suitable for the cut-off analysis of large core fibers with a finite cladding dimension.