First of all my greatest congratulations on receiving 2 offers from top firm. It's amazing and you are lucky one, giving the current situation.
Secondly, I absolutely believe that all three firms are equally leading in general strategy across industries and functional areas. Nevertheless, there are some slight differences in culture and approach that give each firm a bit of a unique profile and flavour. Each also has competitive advantages in certain practice areas that they are known for.
There are some information that might clears up your choice:
- Medium size of the three (~5 or 6K employees), second oldest
- Areas of expertise: Corporate Development, Growth, Innovation
- Industries: Consumer, Financial Services, Government
Reputation/culture: Very academic, innovative; relatively more family oriented
- Smallest of the three (though almost the same size as BCG), youngest
- Areas of expertise: PE/LBO, M&A, Organizational turnaround
- Industries: Financial services, IT, Media/Entertainment, Healthcare
Reputation/culture: Results oriented, innovative, aligns own incentives to clients' performance; social
So, if you have an interest in PE, technology and gaming as you've mentioned, I think Bain in a long term would be better option for you in terms of the exit opportunities.