climate control or a/c

Very rare for a compressor to go. The weakest link is the seals, which go hard if the system isn't used once a month even during the winter (set to heat). Then the gas will leak out and the a/c won't work.

I'm not entirely sure what you're asking. As you say, both Climate Control and plain Air Conditioning have a compressor. Climate Control is just a computer controlled front end to the ventilation system as opposed to having manually controlled dials.With Climate Control you can simply dial in a preferred temperature and the climate control system will adjust the air flow, air conditioning, temperature, etc. to adjust to and maintain that temperature - of course all of these are can be overridden manually. Without Climate Control you would have to constantly adjust the temperature to compensate for changes in outside temperature or radiation (such as the sun going behind a cloud). Or just put up with it. There isn't really much difference in terms of what can go wrong. Although there are more parts to wear out or break in digital air con (such as the motorised valves) and more electronics, they're computer controlled - it isn't going to turn the knob too hard for example.

Digital Climate Control has other advantages over normal manual air conditioning in that it will activate in the winter, even if it's just to demist your windscreen (air conditioned air is dryer as moisture condenses on the cooling unit so helps to clear your windows of moisture faster). This keeps the air conditioner moving parts and seals lubricated.

Or are you asking if air conditioning is reliable in general? These days, for most people, it is. Although it can be very expensive to fix if it goes wrong out of warranty. In terms of it effecting your fuel economy, driving style still has by FAR the greatest effect on fuel economy.

Adam