A couple of comments. I've used pretty much all mandrels over the years, but never the Berea with the MT adapter. So this one I can't comment on.
Re. A vs B size: There should be no argument that B is stiffer. The A mandrel is .246" the B is .290". Larger diameter is stiffer.
I liked the drill driver setup because it's simple, there were always replacement shafts available which I don't think was true 10 years ago if Berea even had a MT2 screw-in mandrel then - I don't recall. The advantage I always saw is that the bushing is a press-fit over a raised dimple, so you can adjust the length a little.
I consider the difference between a $15 and a $20 mandrel totally insignificant...
I used to go through mandrels, but frankly, I don't any more. I do virtually everything on a B mandrel, to the extent that I ream out bushings that only come in A size. I've used the same mandrel for probably 2 years now. I just replaced it, because the tailstock end had mushroomed sufficiently. That was a mandrel I had made, and I used a slightly large center-drill. I can't even tell why I used to replace mandrels... it's been too long! I suspect I bent them... Don't recall. Probably though. Better turning technique maybe by now, better squaring, sharper tools. Anyway, I consider mandrel expense totally irrelevant.
I've heard it said that the high-precision mandrel is hardened. Take a small file and cut a notch at the headstock end and convince yourself that it may be hardened, but not a lot ;-) I also was looking for data that a hardened mandrel should be stiffer and could not support that anywhere.
Beall chuck vs MT: Though I very much like my Beall chuck and would not want to be without it, I think in principle the MT (specifically the drill driver) is more accurate since it references the ground inner surface of the spindle. That is a high precision surface. I am convinced that the nose thread is less precision. And if you think of the way a male and a female thread interact, you can appreciate that there has to be some slop. In my case, the Beall chuck fit is extremely good and repeatable, but I have heard of others where that is not the case, and saw a lathe where that thread was WAY off! So theoretically the MT may even be better. I'm lucky and happy and will continue to use the Beall chuck.
The reason I like the drill driver a little better is that I don't trust the solid MT to be machined to the same precision, and the interface between MT and mandrel, that thread, is again a potential source of inaccuracy. Simplicity wins! I don't mean to say that most solid shank MTs are off by a lot, but if you looked at a large enough smaple of both you'd find the runout distribution of the DD setup to be tighter.
The replacement mandrel I just made is a simple piece of zize L drill rod. The critical step is to drill a perfectly centered hole using a center-drill in the tail-stock end. That is the ONLY precision machining step necessary! Then you can cut down a section to 1/4" and add the thread of your choice - I choose 1/4-28. So if you need a slightly longer mandrel, it's EXTREMELY easy with the Beall chuck or drill-driver, a little more complex with the screw-in mandrel. More precision steps for the interface to the MT! You can get the DD from Berea, or you can buy one from a machineshop supply house, it's a standard part. I think Berea offers these as a convenience.
