You have answered it yourself..McK/BCG won't take you in just because you work for certain brand. Your CV may get through easier if you studied in top schools and/or worked for well know brands. But after that its start from zero. Your CV & application will be looked at in totality- your education, work experience, referrals, cover letter etc all matter. I have seen people from absolutely unknown companies and very quirky backgrounds make it to MBB and they are doing very well.
So please think through this right..choose OW or ADL not because you want to end up McK/BCG in future (which you cant predict) but because one of them is a better fit, will allow you to be joyful and give your best. McK/BCG will happen if you get your moves right.
Enjoy the offers, celebrate the success and work hard.