I'm not sure I ever read the "Katy" series as a youngster. I do have What Katy Did Next in amongst the books of my youth (yes I still have many of them) so perhaps I just don't remember.
Reading the first in the series I found I liked it, although with a few reservations.
I liked Katy and her family. I enjoyed the simplicity of the storytelling that still painted a fairly vibrant picture of the family and the various people they interact with. Although it would have been nicer to learn a little more about them.
I liked the points about "life lessons" and appreciated the point about looking for the positives and appreciating the little things (like filling your life with nice flowers and appreciating the sunlight etc).
My reservations come from my modern-day perspective I think. Especially with things like depression (yet there is often still the mindset that someone falling into depression is "just being selfish").