Congrats on the offers! Full caveat - Wharton alum here with no interest in a career in finance.
For most careers, I'd say that there's no difference between the schools - mgmt consulting, tech, general mgmt. But for finance? And PE in particular? Wharton hands down. Mktg? Arguably, a slight edge to Kellogg - although there's a reason that Wharton is the number two school in mktg.
I think that the key edge that Wharton enjoys is that it has a more active community for PE recruiting - it has more of a critical mass of students, alums and companies that you can benefit from - particularly for something that requires as much 1-on-1 networking as PE (as opposed to the more regular, structured on-campus recruiting that takes place for IB / MC). No disrespect to Kellogg intended, I just suspect PE recruiting is more of an individual endeavor at Kellogg, with less of a community to tap into (OK, maybe a little disrespect to Kellogg's PE/VC community lol).
As a point of comparison - check out Kellogg's PE/VC club (sorry not allowed to post URLs) - it's interesting to me that they have no upcoming events and they haven't finished building their website (see the generic purple box on the bottom right-hand corner). LOL. Just compare the Kellogg to the Wharton PE/VC club - and see how much more active the Wharton club is.
And none of that is necessarily a bad thing. PE recruiting is such an individual endeavor anyway -- it's really down to your individual attributes. So if, for example, you were a shoe-in anyway for a PE career based on your pre-MBA experiences, don't mind/ need the community, and have strong fit with the Kellogg vibe, then by all means -- go to Kellogg and have what will surely be an awesome time.
On the financial front, I'm sympathetic. But I generally agree with others who've suggested you bite the bullet and go to Wharton, given your interest in PE and assuming you can afford to bear the cost. Sitting on the other side of b-school experience, I can say that the debt doesn't last, particularly if you were interested in a field such as PE.
What can you practically do? Don't just rely on random opinions on an online forum - ask both schools to connect you to current students and alums (either who had PE/VC backgrounds before school, are currently recruiting for those roles, or are currently in them). Or just reach out yourself directly to the PE/VC clubs. It'll maximize your signal to noise ratio.
Good luck!