Sorry to hear about this experience. The reality is that it's tough to get into these firms and the recent economic events don't help much either.
To answer your questions:
Are the Big 4 more negative towards PhD graduates?
I'd rather say instead that MBB is more open / interested in PhD graduates. That's mostly because they have a different target client and type of project and they look for people with knowledge spikes in certain areas. Nevertheless, the differences are not huge and they shouldn't show up if you're applying to multiple firms.
How different should be the CV and motivation letter comparing to MBBs?
You can use the same CV to apply to all consulting firms as long as that CV is in a good shape.
My suggestion would be instead to get some help at this point. Let's put the aside the fact that I'm a coach on this platform. The fact of the matter is that your current application strategy does not work and somebody with more experience needs to help you understand why. It's a worthwhile investment especially if you think about the long-term benefits. With the current info you provided in the questions it's difficult to give more specific feedback.
Lastly, job hunting is also a numbers game. So even though I know it's painful to be rejected (I've been there so many times), you just have to keep on going.