Government Energy Star ratings list LG brand at top of efficiency ranking; but not by much. The lowest-capacity window air conditioner with inverter drive I see listed is still 8,000 BTU/hr. The LG has CEER of 15.5, with many other models at 15.0.
In lower-capacity units without inverter drive, it looks like LG 6,000 BTU/hr unit with CEER of 12.4 has highest ranking. Other brands start at CEER of 12.1.
I’m not surprised LG, a very large corporation that also manufactures mini-split A/C, is competitive in either category, and I would consider their products. Main concern with 8,000 BTU/hr inverter window A/C is its larger size and weight; and somewhat the higher cost also; though probably well worth it just for noise reduction compared to mine. Also electrical load on generator would be steady — or more so. That would be of value to me as well.