Efficiency is pretty hard to measure when you're comparing fuels. Electricity can be shown to be very efficient in many uses, but if the electricity must first be created by burning a fossil fuel, then it's often more efficient to use the fossil fuel directly as much energy is lost in the initial conversion to electricity at the power plant.
Residential gas air conditioners were killed by a combination of high initial cost combined with maintenance costs. For safety reasons, cooling systems larger than those in a refrigerator can't pump the ammonia refrigerant directly to the house. This means a traditional gas a/c system must keep the ammonia cooling system contained outside, and then use a secondary coolant system (usually water-based) to transfer heat from the house to the a/c. That means extra pumps and coils, unlike an electric a/c unit which pumps the cooled freon directly into the evaporator in the house. This means extra cost and complexity for the gas system, which reduces the benefit of not having a failure prone compressor.
When I was a kid, my parents bought a house with a Bryant gas a/c unit. It wasn't new, but worked beautifully and had running costs that really were less than a comparable electric system. After a couple of summers, though, troubles began. One summer it had a leak in the refrigerant system which caused it to blow high-pressure ammonia serveral feet in the air for several hours - it was quite spectacular and everyone in the neighborhood knew we had an a/c leak. The only local service for a residential gas a/c system was the gas company, who had installed it in the first place. For a reasonable price they came out and fixed it, and warranteed the fix.
The next summer there were two similar leaks, with similar results. The third summer brought another ammoinia leak, but by then the gas company had discontinued their promotion of residential a/c systems. The would agree to fix the leak, but no warranty on the fix at all. Nobody else in the area (Dallas-Ft. Worth) much cared to service the system either. My parents briefly looked into replacing it with a new gas system, but the cost was much greater than an electric system and obviously service was going to be a continuing issue. So our a/c was converted to an electric system that cost more to run but was at least reliable and maintainable.
I think gas a/c is a wonderful concept for all the reasons noted above, and no doubt the leakage issues have been solved, but until there's a good infrastructure of dealers and knowledgeable service professionals it's going to be a hard sell, especially due to the extra initial costs.
