7 Days in Osaka/Kyoto; Where to Stay?

My family and I (6 of us) will be in Japan for the first time from 18th December to 4th January. We'll be starting off in Osaka, flying into Kansai International Airport and allocated 7 days for Osaka/Kyoto. I've seen a lot of people suggest to stick to one base, but some say it's worth staying in both.

Would it be wise to spend the first few days in Osaka, then switch over to Kyoto? I know they're not that far from each other, but I'd imagine that if we were to go back and forth between two cities every day it might not be as economical considering the travel time and logistics. I appreciate any advice!