Neither.

I just repainted our main level. Our kitchen faces NW toward a wooded lot, so we don’t get enough good natural light. Although we have better electric lighting (some on dimmers) now, I wanted it bright as a work space. Our living room is adjacent, but doesn’t need that brightness. Because they are adjacent, but need different colors I chose two colors that were related - each just one shade different. So, the corners where the colors change just look like subtle changes in light & shadow, while giving each room the different value of light needed while maintaining cohesiveness. It is possible no one color will be perfect for all rooms you’re painting.

Thats a good point. thank you!

I don’t see a grey or blush (more greige), but both work with floor. More importantly, what is your kitchen cabinetry, counter and backsplash like and family room‘s furniture and accessories. If you need more help, providing pictures would be great as undertone will be important.

Consider as well depth of color based on rooms’ lighting and when you narrow down, be sure to test and a warm white could be a good place to start.

https://thehouseofhoodblog.com/white-paint-colors/