Coorg is a lovely hill station with lovely plantations all over. Famous for picturesque views, beautiful peaks, and great weather Coorg is a must visit place. Chikmagalur is a small hamlet filled with great weather, awesome nature and some lovely places to visit. From Coorg Chikmagalur is 4 hours away. My suggestion would be to club both places for both are not only popular but beauty spots of Karnataka
Coorg has more places to visit. I personally liked coorg more. You can visit monestry, dubare elephant camp, nisargdham etc.
Chikamangalur is not very far. you can club both places. In this season you will get to witness the beautiful red looking coffee beans