If you took your car to a BMW dealer, they would put Castrol in it as that is their oil of choice and is supplied in bulk from Castrol.
LL-01 is the old spec longlife oil, LL-04 is its updated replacement and is fine to use in a LL-01 advised car.
Before any nay-sayers come along, my background is in oily engineering and I spoke directly to Castrols Engineering dept about this subject. My Alpina is specc'd as Castrol Edge (originally SLX) 0W30, but she's thirsty (as most Alps are) and uses this stuff at 650m/litre (no I have no engine problems!!) which is a bit tiresome on a run, and also expensive. So I've upped the grade to 5W40 and use Castrol Edge Turbo Diesel in that grade to see what it does oil control-wise. Again, before the nay sayers come along, it's the same oil as for a petrol engine, just just packaged to appeal to DPF-using derv drivers as it doesn't screw-up DPF's, and is actaully a higher spec oil than BMW's LL-04 (meets and exceeds latest VW group spec). If that fails to contol the usage, I'll move onto an xxW50 (undecided yet) or a 50:50 mix of 5W40 and xxW50 (undecided yet) - you can mix viscosities, but stay within brands to keep the additives the same. BMW/ALPINA reckon you can put 10W60 in these lumps, so anything fully syn, longlife and between 0W30 and 10W60 will fit the bill. However, stay as thin as your engine oil spec and usage allows you to.