I've only just started playing around with it. So far I've tried it on data collected with my 294MM Pro and 8" EdgeHD at f/10 - so an image scale of about 0.45"/px. I've tried it on a narrowband HOO image of Mel-15 (with RGB stars) and also on RGB data of M13. I've played around with the sliders a bit, and tried a few of the different checkbox options.
I use it very near the beginning of my workflow, as I don't want to have anything altering the data before the PSF is calculated. My typical workflow is:
Dynamic Crop for getting rid of any stacking/dithering artifacts
DBE if necessary
Channel combination (various different methods)
Image solver if necessary
SPCC
I have tried BXT at each stage of the workflow above... so as the first step, as the step immediately after crop, as the step after DBE, etc.
What I've found while playing around with it...
On its default settings it did quite a nice job on my M13 RGB data. Here are a couple screenshots of the before/after in PI. First is the "before":

Here's the "after":

I've zoomed in quite a bit to show the effects. I did BXT just after SPCC. This is just a standard STF applied.
Like the M13 data, I applied BXT after doing a channel combination of HOO, crop and SPCC on Mel-15. Same default STF applied. Here's the before:

And After:

Stars are tighter and there's considerably more detail visible in the nebulous structure. Just for fun, I maxed out all the sliders on that same data:

Definitely over-sharpened and the stars look a bit... off... almost like it's trying too hard to deal with the halos, and as a result softens the stars. Going the other way (sliding the halo corrector down to -0.50) gives, in my opinion, an awful result on the stars:

It looks better here than it does on my monitor open in PI. There, you can clearly see ringed artifacts around every star where the halos used to be.
Like Russell's other tools, I imagine this one will need to be applied judiciously per image, and there won't be a one-click-fits-all setting.