Thats my method, wood boiler during cold winter, mini split in shoulder seasons (above 20degrees daytime).I think the savings have not much to do with cat or noncat.
It has to do with having a hugely (50%?) inefficient stove and going to a much more efficient stove (75%?).
Not with a 1 or 3 % difference between different types of (modern) stoves. (And I believe that the ultimate record holder in efficiency, regardless of stove size, is in fact a non-cat? Forgot which one.)
I think Peakbagger hits the nail on the head: what BTU needs do you have - at the various times of the year, and what stove can best meet them. You may have to compromise sometimes (i.e. a sweater on or a window cracked) depending on what the stove you choose can do, but minimizing such compromises is what is best to do. That's why bholler asked for how the old stove did - as it's then (a bit, roughly, guesstimated) known how many BTUs you need.
Another way to meet the compromise is to have a (modern, efficient) stove that can't turn down well, and add a minisplit for the shoulder season lower need for heat.