From speaking to many Investment Bankers at recruiting events at Cambridge trying to convince people that IBD>Consulting: the reason they almost all gave is that in IBD, you actually do, whereas in consulting you just advise. Of course, I don't fully agree with this, or I would be in IBD, but to help you craft a compelling argument:
In IBD you have skin in the game, and your work will definitely have an impact in the end - imagine working on a multi-billion merger, and you worked directly and contributed to that deal.
Consulting, on the other hand (for the sake of this story), you provide a recommendation, but there is no guarantee anything will change, or that your work will have impact. Ultimately, you would rather actually have an impact than produce some reports that might or might not be implemented.
Also, one thing you should definitely not mention is better exit into Private Equity. I know someone who mentioned this as a reason for "why are you switching from consulting internship to IBD" at a final round with Morgan Stanley and got rejected, and in the feedback they said the primary reason was they didn't think he would stay for longer than 2 years before trying to jump ship!