Okay i can't think of much more to say about BA, so to sum up i'd say it rates about 5 on the complexity scale, a nice easy-to-play job, not too simple, not too complex.
(For comparison I'd rate the old Panzer General about 4, Steel Panthers about 6, and Combat Mission about 7).
BA has only been released a few days and already the first patch is out, to their credit the designer is listening and talking to people in the BA forum and is taking feedback on board-
http://www.slitherine.com/forum/viewforum.php?f=87
Once the tiny glitches are ironed out I can see BA becoming a big seller among the majority of wargamers, although old fart 'serious' gamers might be put off by the slightly cartoony graphics.
Personally I only have 2 real gripes-
1- The map view system isn't flexible enough because you can't elevate the view to look towards the horizon, meaning that in 3D view your eyes are fixed at 45 degrees looking down at the ground all the time.
2- A couple more zoomout levels are needed in the game because at the moment you can't zoom out far enough to see the whole map, so you have the hassle of scrolling around.
1 and 2 therefore give me the very uncomfortable feeling of playing with blinkered 'tunnel vision', so for that reason I myself am regrettably out as far as being a loyal BA disciple is concerned..
EDIT- Version 1.3.5 has just added an unlimited zoom option