I will answer based on real world experience.

ADAS-Cog12 is more time consuming to administer, requires more training, is more sensitive to detecting cognitive changes across multiple domains.

The MOCA is quicker, less sensitive, and suffers from a ceiling effect (ie. you can have a score in the normal range and still have impairment in cognition).

Bottom line if you want the more sensitive instrument in a trial to pick up improvement (or lack or deterioration) in cognition the ADAS-Cog would be the way to go.  A good analogy is a chest x-ray (MOCA) vs a chest CT scan (ADAS-Cog).