Purdue Engineering VS Applied math, engineering and Physics (AMEP- LSA) Wisconsin Madison

Hi, my name is Mohit and I’ve been accepted into both Purdue and Wisconsin-Madison. I’m having a really hard time picking between studying Mechanical engineering at Purdue (at the engineering school), and the AMEP program unique to Madison (at University of Wisconsin’s college of letters and sciences.)
Purdue is ranked very high in engineering and getting a BE in mechanical engineering from there would be great for future job opportunities. However, the AMEP program seems perfect for me as I do see myself as a math guy. The only problem with AMEP is that it is in the college of letters and sciences and ill be getting a BS instead, which is not as prestigious.
I’ve visited both campuses and I do love Madison as it is a beautiful campus and lovely city. I could see myself spending 4 years there. However, not that there was anything wrong with West Lafayette, it just looked a bit dull when I was there. I do like to party and Madison seems to have a better party life but I’m not sure, it would great to have people’s input. I’m starting to think that maybe I should have applied for the engineering school at Madison. Is the AMEP, and what I think is a better campus life worth risking an engineering degree from Purdue?
I’m also currently applying to the honors program at Madison and if I get that, it would further cement my place at Madison. The only problem with that is that the decision for that will come out after the enrollment deadline.

Any comments would be appreciated thank you.