Yes, heat is heat. A pure cat insert can burn low and slow, which will help keep the room more comfortable, but that has nothing to do with heat distribution throughout the house.No such luck on the basement.
Do you see this being the case regardless of stove? Treating size as a constant, would this issue be the same regardless of freestanding/insert, steal/soapstone, no-cat/hybrid/cat? I've only ever used a standard steal stove this exact issue was why I was looking at soapstone and/or cat and hybrid options.
The family room is going to be warmer than the kitchen. How much warmer is TBD it might only be 5º warmer which could be quite tolerable. With its peaked ceiling one option would be to scavenge heat at the top of the ceiling and duct it into the upstairs hallway via the spare room with a quiet blower on a thermostat.
What is the primary heating system in the house?