Why don't you do 3-4 days in Goa and 3-4 days in Kerala?
Get your beach time in Goa, then take the train down to Kerala and stop in Kochi/Cochin. Spend a day there, then go to Alleppey and do an overnight houseboat on the backwaters. The backwaters are fantastic. You can take a speedboat from Cochi to Alleppey or drive.
If you don't want to travel so much, then fallingleaves is right. Kerala is more about history, nature, temples, relaxation, great food. HOWEVER, Goa has more to offer than just beaches. It also has portuguese history, catholic churches, hindu temples, forts, historic old city of Panjim, good food.