This is almost exactly the same question I had before buying the 120d (except that X-drive was not available for the F20 then).
I tried to spec the cars to the same level, but found that a lot of the good stuff on the F20 was not avalable on the Countryman SD. On the other hand 4WD was not available on the BMW by then.
I would not spend any money on automatic transmission on the Mini, it has a terrible price. On the BMW it is not avalable on the X-drive so far anyway.
In total the Countryman SD ended up as a cheaper choice, and it is a cooler car imo.
So why did i buy the 120d instead?
I had a car crash with my F12. This motivated me to get rid of the Smart I had as my daily driver and get a new and more safe car. I asked the body shop (which is a specialist on Mini, BMW and Porsche) about differences in steel quality, build quality, paint quality, strength and durability of the body. They recommended without any doubt the F20 instead of Countryman.
Even though the Countryman SD is a sporty car in it's class, it is far from the handling and sophisticated feeling in the BMW. The interior quality and materials are at least one class higher in the BMW.
Finally the engine is a different version of the 2-litre. It runs smoother and of course has more power.
All in all so many factors pointed at the F20. I found the only advantage of the Countryman was the cool factor. Which was not enough to convince me
