I'm guessing AXA.
Measure the height from the top surface of your compound slide (where the tool post would sit) to spindle centerline on your lathe. If you have over 1-1/8" you'll be able to use a BXA with it's standard max capacity (5/8" shank tools).
If you have less than 1-1/8" AXA would be the better choice (you'll need at least 15/16" to use 1/2" tools with AXA). You won't notice a difference in rigidity between AXA & BXA in this case. Only real advantage you'll gain with BXA is that you'll get to use 5/8" shank tools & there are more indexable tools available in 5/8" than 1/2". But there's ways around that, you can mill down a 5/8" shank to 1/2". If you only use tool bits that you grind yourself, again no advantage. But if you can fit BXA properly might as well.
And before you think of it, using a BXA tool post with just 1/2" tools if you can't fit 5/8" will also have no advantage over AXA. And if AXA is the correct size you'll save money on the tool post & holders since they're cheaper.