Neither of those would be a good choice for a whole home flooring. If tile is your choice for climate reasons, look at something not trying hard to be a fake marble. Something quieter. No gloss, unless it has a good non slip rating. Or you have it maintained by a flooring service for upkeep that includes periodic application of a non slip treatment.

Sigh...That is such a personal decision. You obviously love the tile so here's my opinion.

Appearance, I'm not overly impressed with the porcelain tiles made to look like polished marble. I prefer the matte of your two finishes.

I live in the southern states, so hard surfaces such as tile are increasing greatly. As far as practicality with kids, I don't see a problem at all. Just keep your floors clean, clean up spills as soon as possible if/when they occur and have them professionally cleaned as needed and they will provide years of enjoyment.