I had DAB in my last 2 beemers and also have it in my current A4 quattro.
My experience is that in northern England you only loose it in fairly remote places such as the top of the Scotch Corner to Penrith road but in Scotland when you get north of Edinburgh or Glasgow it's pretty patchy.
One of the good points of the Audi is that it auto drops to FM if you loose the DAB. This didn't happen on my E90 325d but I would have hoped BMW would have got the F30 up to date with this technology.
EBII F30 330d xdrive with Pro Nav, Vis Pack, Adaptive, HUD, HK, Electric Seats & Mirrors