Those are completely orthogonal concepts.
- APS-C is a sensor-size. Other sensors for DSLRs are Full-Frame or APS-H.
- CMOS is a type of sensor. Other sensors are CCD.
One can have an APS-C CMOS sensor, an APS-C CCD, a Full-Frame CMOS or Full-Frame CCD. Any combination is possible.
The discussion is almost moot now because nearly every camera on the market uses CMOS now, since the fabrication process is simpler and those sensors can be read much faster than CCD ones. Among very low-end cameras there are still CCDs, and up to recently, some Medium-Format cameras also used CCD but AFAIK, all current DSLRs and mirrorless cameras use CMOS sensors.
This means that if you buy a new DSLR or one made in at least the last 5 years, it will have a CMOS sensor. The choice which is left between APS-C and Full-Frame. The latter is more expensive but also delivers better image quality, particularly in low-light.