what should I do?

I have received an exploding job offer as a strategy & development analyst in a major corporation (need to respond them back verbally in 24 hours). I also have received some "kind words" from a boutique IB (had 3 rounds of interviews, and in background check stage right now); they say they have full intention to move forward (hence the background check), and they are not in hiring free. However, they are unwilling to indicate what's after the background check, eg. job offer. Should I accept the strategy & development job offer if the boutique remains indecisive tomorrow? Thanks a lot!