Last year I visited the MB museum in May and the BMW one in August.
Although I really enjoyed both museums, the former was a much better experience overall (as well as €2 cheaper). Apart from the fact that it is absolutely massive (about twice the size of the BMW museum), the MB museum allows the visitor to understand how industry, society and history have evolved from 1886, through the very privileged perspective of the oldest car manufacturer in the world.
I spent 5 hours on the first day and about 3 on the second and if it was a bit closer to Cheshire I would go there again tomorrow.
Please do not get me wrong, I also loved the BMW museum, but that is just a place for petrol-heads like me, as it is just about cars and motorbikes, so if you are not into them (or if you are with someone who could not care less about them), it could be a bit boring.