based on my experiences at McKinsey and based on some friends from BGC experience I can tell you the following about the MBA (that seems an important factor for you). In the Milan Offices, McKinsey does not have a lmited numbers of sponsorship for the MBA, while BCG does. So basically, at McKinsey you do not compete against your peers, you only compete against yourslelf trying to always excel in your performance in order to receive good reviews and being sponsored for the MBA, in BCG based in which percentile (compared to your peers) you are positioned, you may be sposored or not for the MBA.
In relation to the kind of environment, I guess it cannot be generalized that one place is better than the other, it really depends on the people you are working with.
Hope it helps! :)