There are only very few reports on the effects of concentration in thin film silicon-based solar cells. Due to the presence of midgap states, a fast decline in fill factor was observed in earlier work. However, with the advent of more stable and lower defect density protocrystalline silicon materials as well as high quality micro-/nanocrystalline silicon materials, it is worth revisiting the performance of cells with these absorber layers under moderately concentrated sunlight. We determined the behavior of the external J-V parameters of pre-stabilized substrate-type (n-i-p) amorphous and microcrystalline solar cells under moderate concentrations, between 1 sun and 21 suns, while maintaining the cell temperature at 25oC. It was found that the cell efficiency of both the amorphous and the microcrystalline cells increased with moderate concentration, showing an optimum at approximately 2 suns. Furthermore, the enhancement in efficiency for the microcrystalline cells was larger than for the amorphous cells. We show that the Voc’s up to 0.63 V can be reached in microcrystalline cells while FF’s only decrease by 9%. The effects have also been computed using the device simulator ASA, showing qualitative agreement.