For perspective, I worked 5.5 years at BCG in Germany and Japan, and did projects all over the globe. I have multiple friends at both McK and Bain. The following are my personal views, and your statement "from different online sources, I am getting different ideas" also holds in "real life" :)
(1) The differences between all three firms (and even other top managment consultancies) are negligible compared to non-consulting firms/jobs.
(2) All three firms have grown so much, they compete on all levels and no longer specialize in certain topics or industries. Basically, if one of the firms pitch for a certain project, the others could do it equally well.
On to the differences:
- In Europe, there is still a difference between McK/BCG and Bain, which is a bit smaller. So, while any competitive pitch where McK is invited also has BCG pitching (and vice versa), Bain is not always present.
- McK tends to have a more top-down, slightly harsher approach (maybe rooted from operations/cost cutting experience). BCG has a bit more cooperative approach, building support bottom-up together with the client's organization/middle management. Bain is somewhere in the middle.
- I found the smartest/most intelligent people to be at McK, intellectually a tiny notch above the other firms. BCG I found to be a bit more creative/out of the box.
Again, all of this is highly subjective. If you receive an offer from any of the firms, congratulations, that's amazing! :) If you end up getting more than one offer, I would choose the one which feels the best to you personally. I loved BCG, but one of my friends did not like the atmosphere and they somehow didn't connect -- he is now super successful and happy at Bain. During the interview process, you get to know 5-10 consultants over 2 rounds in a professional context. And keep in mind -- they don't just interview, but also try to make a good impression on you! The interview process is actually quite revealing about how working there would be, so going with your gut feel is probably the best way to go.
Good luck and all the best!