Main differences between the BAS and M-43 would be blade shape, handle style, and, mostly because of the other two, balance. Overall size too I guess, since the BAS is most commonly seen in 15".
The M-43 has more belly to the blade, which I prefer, and can be found in a wider length/weight range. My very first HI khukuri was a 15" 26oz BAS, which is now residing with one of my best friends up in ME. It was/is a great blade, but I prefer wood handles to it's horn, and it didn't have quite the belly I like.
Handle style on the M-43 is a "full tang" construction with handle scales pinned on, as opposed to the traditional "kangaroo-tail" construction with one solid piece of wood for the handle. I actually like traditional better, and if I were to change one thing about the/my M-43, that would be it. Due to having more steel in the handle, an M-43 of the same specs as a BAS will balance slightly more towards the handle, generally speaking. Plus the handle on the M-43 has a slight curve, compared to a straighter BAS handle. Oh plus the BAS has the ring on the handle, some love/hate it, others like me have no preference (yet...).
Now bear in mind I'm comparing from personal experience, which in my case is a 15" BAS and a 17" M-43, and it's not always accurate to compare blades of different lengths. Not to mention the fact that every single blade will feel different, even my 2 KLVUKs feel and look quite a bit different.
What I will add is that this thread is one of the first times I've seen such a unanimous recommendation in any blade other than a KLVUK. If I'd had an M-43 sooner, I probably woulda been recommending it too! I know Bookie can also throw his M-43 quite well. Perhaps I'll get there eventually.
And thanks Mateos and BB! Passed up many other fine versions, but I do believe this is my favorite in recent months! Gotta touch up the handle then I'll do a real post on it.
BB, got more foam and such, just gotta find time to make the new press! Gonna try this M-43 first, if it's a success I'll be good to go