The calculation of X-ray emission spectra has been addressed with the algebraic diagrammatic construction (ADC) scheme, using a core-ionized wave function as the reference state. With this, the valence-to-core transitions are found as the first eigenstates with negative eigenvalues. The performance of the ADC hierarchical methods ADC(2), ADC(2)-x, and ADC(3/2) has been investigated on 17 transition of second row elements (C, N, O, F, and Ne), and 5 transitions of third-row elements (S and Cl). We report ADC(2) results within 0.20 +/- 0.36 eV of experimental values with an appropriate choice of basis set and when accounting for relativistic effects, with a slight tendency toward underestimating emission energies. By comparison, ADC(2)-x yields a similar spread in relative energies, but a consistent overestimation of approximately 1.5 eV. Going to ADC(3/2), we now observe an underestimation of emission energies and a larger error spread. By comparison, calculations of X-ray absorption spectra have been reported to favor the ADC(2)-x method, with ADC(2) showing the largest error when comparing to experimental values. The difference in ADC performance trends between these core spectroscopies are attributed to the different electron rearrangement effects in X-ray absorption and emission processes.