The effect of quantum degeneracy on the work output from a Stirling cycle working at quantum degeneracy conditions (QDCs) is analyzed. Expressions for net work outputs of Stirling power cycles working with monatomic ideal Bose and Fermi gases are derived by using the quantum ideal gas equation of state. Ratios of net work outputs of Stirling cycles working with Bose and Fermi gases to the net work output of a classical Stirling cycle ${\mathrm{(R}}_W^B$ and $R_W^F,$ respectively) are obtained. Variations of $R_W^B$ and $R_W^F$ with $T_H$ are examined for a given temperature ratio ${\mathrm{(\tau =T}}_L{\mathrm{/T}}_H)$ and a specific volume ratio ${\mathrm{(r}}_{\nu }{\mathrm{=\nu }}_H{\mathrm{/\nu }}_L\mathrm{).}$ At QDC, it is seen that $R_W^B$ has a maximum value, which is greater than unity. On the other hand, there is no maximum or minimum point for $R_W^F$ and $R_W^F\text{⩽1}$ for any values of $T_H.$ Consequently, the use of Bose gas as a working fluid in a Stirling cycle provides an advantage since it causes the net work output per cycle to increase by consuming more heat energy. This fact is seen to be in the opposite direction for a Stirling cycle working with Fermi gas.