I suspect you've just not noticed that both gauges are installed in a lot of --maybe most --airplanes. They measure two entirely different things, and are used for two different purposes.
Exhaust Gas Temperature gauges measure the temperature of the exhaust gas, usually with a probe located just outside the combustion chamber in the exhaust stack. If an engine is running with a fuel mixture that consumes all the fuel and all the oxygen in the charge, it is said to be "stoichiometric," and the temperature of the exhaust gas will be at its hottest value. If we either enrichen or lean from that point, the exhaust gas gets cooler. Air cooled engines, in particular, use excess fuel to cool the engine down. If we put in too much fuel, the unburned fuel evaporates and cools the engine in the same way that your skin cools if it is wet and air blows across it. Above some power setting, usually 75 to 80 percent, there isn't enough fin area on the cylinders to keep the engine cool, and the excess fuel is the only thing that keeps the engine from overheating and being damaged. During takeoff and climb, we operate with an intentionally rich mixture for this purpose, but once we reduce to cruise power, we can lean the mixture to save fuel. Most airplane engines cruise at 50 to 100 degrees Celcius on the rich side of peak, though you should check your own engine to see what is permitted. This is done, operationally, by first reducing power to a power setting where leaning is permitted, usually below 75%, then slowly pulling the mixture control back (leaning) until the EGT reaches its maximum value and starts to fall off. The mixture is then enrichened so that the EGT cools 50 to 100 degrees below peak. At very low power settings, usually below 50 percent power, you can run at peak. Some special applications can run on the "lean side of peak," but most engines would be damaged by doing that. The EGT allows accurate leaning, though there are other, less precise ways to doing it.
The Cylinder Head Temperature gauge, on the other hand, measures the temperature of the metal of the combustion chamber, usually using a probe that either screws into the cylinder head, or fits under a spark plug. Many things influence CHT, such as power setting, fuel mixture, airflow, etc., but it is relatively slow to change, compared to EGT, and would never respond quickly enough to be used to lean the mixture. It is more of a general condition indicator. It is calibrated to give the actual temperature of the metal, where EGT only gives an indication of how much the temperature has varied away from the peak temperature.
Sorry about the long explanation. When someone asks me what time it is, I tend to tell them how to build a clock.
Dr. Rob