Depends on the what you want to find out by comparing their thermal emission. Different variables will probe different characteristics.
For instance:
1) If you want to compare their Thermal Resistance to the rest of the Universe it's probably easiest to use the same power.
2) If you want to compare their surface Emissivity then you want them at the same temperature.
3) If you want to compare their Thermal Emiission Spectrum to each other then use whatever yields different temperatures of the two devices.
4) Something else?