I've got one on a 10" logan that came with the lathe. After having used it, I would prefer to have had an AXA. On the 10", I'm at the bottom of the adjustment range when setting height on most tools, and cannot use 1/2" tools because of it.
Since your lathe is that much shorter, I think if you have a choice, that you should go with an AXA.
The swing of the lathe actually has little to do with the tool post size you require. What matters is the vertical height dimension from the center of the spindle (or tailstock center) to the top of the compound slide. Yes, manufacturers list lathe swing sizes for their tool posts, but it is not really a good way to choose a tool post size. (Some lathes have carriage/cross slide/compound combinations that are higher or lower in relation to the spindle axis than other lathes with the same swing.) At the risk of confusing you even more, the size tools you use or plan to use can also enter into the equation. What you want to end up with is not running out of vertical travel with your tool post when putting each and every one of your tools at spindle center height. A few of the manufacturers do a better job of explaining this than others do, but most tool posts are clones of others, so the data can often transfer to other brands.
Probably AXA for that lathe, but again, it ain't that easy, if you want to makes sure you will be happy with your purchase. I don't know how many I have seen buy a tool post and a bunch of holders, and then change to another size. Try to get it right the first time by getting your head around what you need for what you do and study what is available. And, yes, it will take some thinking, researching, and measuring. You know, machinist stuff.
Or you can guess or flip a coin...
I have no idea what the spindle center line to top of compound is for your lathe, that dimension is not given in lathe specs.
You will ONLY use 3/8" tools on that lathe, never anything else? Ideally, everything you will ever mount to the tool post must fit the size tool post you install...
Go to the Shars site and find the tool posts and just pick one for a start. They show how to measure your setup. I have a 12x36 Craftsman with the commercial compound which is about 1" lower than the non-commercial version. I ended up with the BXA but if I had the taller non-commercial compound the AXA would have been better. With the BXA I have some up and down adjustment. Had I chosen the AXA the tool holder would probably have been all the way at the top with no room for vertical adjustment.
And just a heads-up, my compound has what must be an unusually narrow t slot. I had to make a custom center mounting bolt because it was too big for my t slot and t slot nut. It was fairly easy to make.
I have an AXA on my SB Heavy 10L. Some of my tool setups require the holder to be adjusted all the way down to get to center. I wouldn't want a larger toolpost and certainly wouldn't recommend a BXA on a smaller lathe. You will be constantly fighting it.
Just goes to show... My 12 X37 lathe only has room for an AXA, and barely enough vertical adjustment with a 1/2" tool in it! To use my .600 tools in it, I have to mill out the bottom of the holders and adjust all the way down... I don't think I could use even a 3/8 tool in a BXA on my lathe. The reason is that the compound is so very thick that there is little room for the tool holder. and adjustment.
What you need to do is to measure from the top of the compound to the centre line of the lathe. Take the centre of the tool post and imagine the centre line on it. then transpose a tool holder and see if you have enough room for tools! (wow that sounds complicated!
BTW you can also get XL holders in both AXA and BXA, which further complicate the whole calculation...
P.S. I milled my carbide holders so I can use them in my 4 way without shims, and use it/them 60% of the time. I only use my AXA for HSS tools these days!