Some years ago Multiple Quantum Wells (MQW) solar cells were introduced as an alternative to obtain high efficiencies. Based on the simple Shockley diode model, the short-circuit current could be increased without loss in the open-circuit voltage. Applying the Detailed Balance Theory, including radiative recombination in the i-region, leads to less optimistic predictions of the limiting efficiency of MQW cells. We present an experimental study in order to compare the efficiency of MQW solar cells with heterostructure cells with graded Al compositions and single bandgap solar cells. Compared to the homojunction AlGaAs cell, an increase of the short-circuit current is observed by the incorporation of GaAs in the i-region. However, the open-circuit voltage is reduced by the implementation of GaAs, due to an increase of the non-radiative recombination current. To estimate the maximum possible open-circuit voltage, the radiative recombination current is determined by measuring the light emission as a function of the applied voltage. From this experiment we conclude that the maximum possible open-circuit voltage of all the heterostructure cells is considerably lower than the homogeneous AlGaAs cell and close to the value of the GaAs cell, showing the relation between the open-circuit voltage and the smallest bandgap in the cell. The measured curves can be well predicted by calculations based on the Detailed Balance Theory. We find no principal advantage of MQW cells over cells with graded composition or single bandgap cells.