how do aircraft engines compare to car engines for reliability generally?
Most car engines will make over 100,000 miles without any mechanical rectification. That is about 2,500 hours of operation, ignoring periods at idle, which adds to making a comparison complicated. Most aero engines will do well to get to 1,600 hours without a top overhaul, and a major overhaul by 2,000 hours. On that basis the car engine is vastly more reliable.
The engines are, as others have said, operating in very different environments.
However, my knowledge of performance cars would leave me to believe that lubrication and heat are the two most important factors in determining the life of a well built engine. While a road car may operate a great deal of its time at low rpm the aim of a race car is to operate continuously in its maximum power band. That will almost certainly mean between 5,000 and 8,000 rpm. In the case of a car add a few G in corners and it is all to easy for the engine to be starved of oil. For this reason we fit dry sumps, in some ways not dissimilar to the Christen systems on aircraft. Without these systems it is quite possible to destroy an engine in a single race. In a similar way light weight alloy car engines are hugely susceptible to excess heat. A loss of coolant will destroy a hot engine in a minute or two. We cringe when you watch novices starting the engine from cold and immediately applying throttle. Not only has all the oil found its way to the sump but it takes 5 seconds or so for oil pressure to have established even with a dry sump. In this 5 seconds a great deal of damage can be done.
The engines we use day to day in our cars are way short of the power the engine is capable of producing. The tolerances are large and the stress on the components is kept to a minimum. Despite what the advertising agencies may like to tell us the name of the game is to deliver an engine that is no where close to its peak performance capability, because by doing so it will be reliable. My 1600 engine in its usual road going guise develops less than 100 bhp, in some sportier cars that is pushed to 120 bhp. The same engine with hot cams, ported head, forged pistons and properly mapped will produce over 200 bhp - twice the power.
In some respects aero engines are no difference. On the whole the mapping is rudimentary and the engine is not designed to operate close to its potential. However, there is an equally big difference. I can easily apply +6-4g to my aero engine. I can easily chop the power, and without any thermal buffer from the water cooling system in my car engine expect the air flow to dissipate all the heat from beneath my tightly cowled engine. I can easily expect the engine to sit idle for two or three or four weeks, start the engine, and expect it to provide maximum power within 10 minutes of startup whilst also expecting it to reach its full operating temperature in the same time. In short even when we are kind to aero engines we give them a load of abuse. As to the original topic of the thread this is one of the reasons twin engine aircraft should be more kind to their engines - it is far easier to dissipate excess heat in a twin than in a single.
I reckon if you used your aero engine every day, always allowed at least 5 minutes to fully establish oil pressure, avoided shock cooling and any manoeuvers likely to restrict oil flow aero engines would do nearly as well as car engines.