This a bit of an apples and oranges comparison. To dissipate an equal amount of heat, an air cooled solution will need more weight in radiators near the antenna, whereas liquid cooling offers much more flexibility in the location of radiating surfaces.In the other hand, air cooling is easier to implement, light and may have little impact to the aircraft's structure, thus why those AESA upgrades for legacy fighters are typically air cooled.
With the important simplifying assumption that the TRMs and backend signal processing are the same. More TRMs mean a larger antenna aperture, power and gain, which is why the PA product is a useful yardstick for comparing radars of similar tech levels.However the main driver of AESA performance would be number of TRM's as the performance gain, scales by cube of TRM. Radar that can pack more TRM's than the other will usually "win" in terms of performance. Radar with less number of TRM's when trying to match the performance of the radar with more TRM's will be "penalized" in cooling and power requirement and thus cost.
However, state of the art AESAs with wide bandwidth, digital beamforming and more sensitive receivers can easily have superior performance over older analog AESAs from the early 21st century, especially once environmental factors like jamming are brought into the picture.