Both are fantastic schools and I'd advise you first and foremost to visit each school. Next, I'd think about where you'd rather live. You mention that moving to Boston could be a rude awakening; does this mean you would rather be in Chicago long-term? If so, Booth is obviously a powerhouse in the Midwest.
As a current Sloan student, I can't give you much perspective into Booth's offerings in entrepreneurship and analytics, but I know a lot about what Sloan offers.
In terms of entrepreneurship and startups, the resources here are overwhelming. Entrepreneurship is so prevalent that it makes folks who aren't pursuing it (like me) wonder what they are missing out on! There are lots of programs in place to support budding entrepreneurs and to help connect Sloan students with students from other MIT programs and other schools in Boston. Some examples include: the Martin Trust Center for Entrepreneurship, the MIT 100K Competition, numerous hackathons (HackFit, Hacking Arts, Hacking Medicine), the Entrepreneurship & Innovation (E&I) Track, and the E&I and Coders Clubs.
In terms of analytics, one of the things that the Sloan faculty pride themselves on is looking at management issues using an analytical framework. In our first-semester core, we take three fairly quantitative classes: Economics, Financial Accounting, and Data, Models, and Decisions. There also lots of follow-on analytics classes offered for your final three semesters. Here are a few that I've heard awesome things about that you might want to look into (
https://web.mit.edu/catalog/pdf/course_15.pdf): The Analytics Edge, Statistical Consulting, Pricing, The Economics of Information, Customer Analytics, Introduction to System Dynamics. And that of course says nothing about all the non-Sloan MIT quantitative classes you can choose to take.
On a personal note, I was invited to interview at Booth after I got into Sloan, but decided to withdraw my application. Most notably, I wanted a smaller class size (400 vs. 550) and wanted a flexible curriculum, but not to the extent that Booth offers. Obviously, there are arguments to be made in favor of both sides, but I just wanted to share the most important reasons on why I chose not to pursue a spot at Booth.
So yes, Booth is a great school with many strengths, but don't count out Sloan just yet!