Centre height is of little importance. The distance from the top of the compound slide to centre height is important.
You need to be able to mount the largest of your tools at centre height, so subtract the distance between cutting edge and bottom of the tool from centre height to compound surface. What's left over is the maximum thickness for the bottom of the tool holder.
In looking at Chinese made piston tool posts at Chronos Tools on Saturday, I saw no difference in the thickness of the base of the tool holders between the small vs medium (100 vs 200 or AXA vs BXA) sizes. The choice then would be based on the width of the post compared to the width of the compound slide.
Tool holders by the various manufacturers vary and you should check dimensions.
I use both AXA and BXA on my 12". The AXA would be my choice for your lathes.
My vote - AXA
I have a 12" Nardini lathe and a BXA size tool post. The BXA is OK for regular turning tools and this WONDERFUL 1" boring bar ($10 with several extra inserts at the CAMA festival) that I have. It's too tall for the standard parting tool holder, though. I have to mount the parting bit upside down and run the spindle in reverse.
If I was doing it over, I would have gotten the AXA size. Just my $.02
I built an AXA size for my 10 inch Sheldon, works great.
I have a Jet 10" swing lathe that has a BXA post on it, as well as a 10" Sheldon that has an AXA. I honestly cannot see much difference in the rigidity between the AXA and BXA that would matter on a machine in that size range. The BXA does on rare occasion seem "in the way" for some work.
I tried the BXA on the Sheldon, but it seemed bulky and out of proportion to the topslide of the machine, so I went with the AXA on that lathe. It has never seemed to be any sort of limitation. Works great for me.
Several posts agree that you need to choose a toolholder based on your compound-top to centre distance. But no one has posted what theirs is.
I claim to have the lowest tool ceiling around. I have 11mm - a tad less than 7/16ths - from my compoud to my centre axis.
I could take 1/4" or so off the top of the compound, but I'm reluctant to do it.
I can't really see myself being limited to 1/4" tooling, and that would give me only 5.32 of floor thickness for the QC holder. I much prefer 5/16" tooling, so no holder for me. I blame my Lorch.