Electrical and galvanomagnetic measurements, made on modulation delta-doped-(Si) Al0.37Ga0.63As/GaAs and In0.34Al0.66As/In0.36Ca0.64As heterostructures, fabricated into modulation doped field effect transistor-like gated Hall bars, were used to determine their DX center energies and densities in the normal and persistent photoconductive mode. Self-consistent Poisson/Schrodinger simulations of the gate voltage dependence and of the temperature dependence of the charge transport parameters of these heterostructures provide the position of the Fermi levels in the barrier layers, E-FB, relative to the conduction band minima and the electron densities in their quantum wells. The energy, E-DX=0.14 eV of Al0.37Ga0.63As determined from the temperature independent equilibrium position of E-FB is consistent with the average of the three lowest DX center energies of this alloy. It is also consistent with that determined by others, on epitaxial Al0.37Ga0.63As layers, using conventional Hall measurement, deep level transient spectroscopic and hydrostatic pressure measurements. Strain relaxed In0.34Al0.66As/In0.36Ga0.64As heterostructures, grown on GaAs substrates, were used for similar measurements and simulations. These yield the energy of the DX centers in In0.34Al0.66As, relative to its Gamma-valley minimum, E-DX = 0.18 eV. This value in conjunction with the previously determined DX center energies of AlAs and that of In0.52Al0.48As, above its conduction band edge, E-DX(x) is correlated with, but not identical to, the composition dependence of the L band of InxAl1-xAs.