In this paper, we compare Stirling and Ericsson cycles to determine which engine produces greater net work output for various situations. Both cycles are for external heat engines that utilize regenerators, where the difference is the nature of the regeneration process, which is constant volume for Stirling and constant pressure for Ericsson. This difference alters the performance characteristics of the two engines drastically, and our comparison reveals which one produces greater net work output based on the thermodynamic parameters. The net work output equations are derived and analysed for three different scenarios: (i) equal mass and temperature limits; (ii) equal mass and pressure or volume; and (iii) equal temperature and pressure or volume limits. The comparison is performed by calculating when both cycles produce equal net work output and then analysing which one produces greater net work output based on how the parameters are varied. In general, the results demonstrate that Stirling engines produce more net work output at higher pressures and lower volumes, and Ericsson engines produce more net work output at lower pressures and higher volumes. For certain scenarios, threshold values are calculated to illustrate precisely when one cycle produces more net work output than the other. This paper can be used to inform the design of the engines and to determine when a Stirling or Ericsson engine should be selected for a particular application.