Interesting question - I spent nearly 4 months thinking about this from the time I initially was accepted into Harvard early action around December 15th till the day I committed to Harvard. I was deeply appreciative of the exciting choice I faced and am sure that no matter which of these places I chose, I would have had a great experience. I also consider Wharton in this mix as well. In saying that - how did I choose?
Firstly, education is an investment in yourself and your future. It is important to consider the reputation and resources of your university and how you might be able to contribute to them and develop as a learner and a leader. I started by consulting a lot of rankings:
www.timeshighereducation.com
World Reputation Rankings
The Times Higher Education World Reputation Rankings 2016 employ the world’s largest invitation-only academic opinion survey to provide the definitive list of the top 100 most powerful global university brands.
http://www.usnews.com/education/best-global-universities/rankings
All the universities mentioned above are utterly incredible and would be a true privilege to attend. However, you have to start any decision from data initially so these rankings let me make my first cuts which were Columbia and Duke. Columbia and Duke tended to underperform need-blind Ivy League schools with larger endowments as well as both Oxford/Cambridge and MIT/Stanford and reputation rankings tended to support this.
Secondly, I considered what country I wanted to be in. Simplifying what was a very complex decision, I decided that the global hubs of finance and entrepreneurship were in New York City and Silicon Valley (USA) and these hubs tended to be growing faster in influence and talent than the UK. This is debatable obviously but generally based on cross-yield data and international applicant numbers to respective countries, as well as considering where most massive companies and organizations have their HQ (Goldman Sachs, United Nations, Facebook, Google, Microsoft, Tiger), I felt reasonably confident that the US was a better bet. Also, coming from New Zealand, the UK was a more easy, comfortable cultural fit and I actively wanted to challenge myself. Lastly on this point, US schools have financial aid for international students meaning the cohorts are more diverse generally making for a more interesting experience. For these factors, I cut out the UK and Cambridge.
At this point, I am considering Harvard, Penn (Huntsman), Princeton, Yale, Stanford.
I actually signed up for university preview tours (the 2-3 day events colleges put on for pre-frosh [students admitted considering entering into freshman year]) for all of these universities and headed to the US with my Dad.
Upon going to Princeton, I realized that I didn’t want a small town vibe in my university experience. Princeton is location in Princeton, New Jersey which is about 1 hour from New York City. I figured if I was traveling all the way from New Zealand to the US, I may as well fully immerse myself in both an intense academic and metropolitan environment. Despite Princeton’s epic academics, leading endowment per capita and very attractive ORFE program, based on the physical campus and where it was located, I gave it the cut.
Yale’s preview event “Bulldog Days” was mind-blowing, fun and informative. I thoroughly enjoyed it and made a lot of good friends who I still talk to a lot these days. My main qualms with Yale were the relative weakness in engineering, pure mathematics, computer science and statistics which were all areas I was very interested in pursuing. I also felt that Yale had a very big focus on “happiness” and “balance” over “ambition” and “competition” to the extent that it seemed almost a bit too relaxed. Lastly, I felt if I wanted to go to a place with so much gothic architecture, I may as well have gone to Cambridge (https://www.youtube.com/watch?v=EqsTatw-RTI). I must admit that having gone to Harvard my post Yale reflections may be just a little bit biased… 
Yale gets cut.
Next came Stanford. To be honest, Stanford is pretty phenomenal at virtually everything these days. Living on the West Coast and the East Coast are two very different environments. The former has quite a focus on venture capital, high technology, entrepreneurship and has delightfully sunny weather. The latter has quite a focus on government, hedge funds, investment banking, management consulting, biotech (although big hubs in SF) and bounces between searing summers (in the 20 to 30 C range) and freezing winters (-5 to -15 C range). Computer Science is a massive part of Stanford’s campus culture just like Economics/Government is a massive part of Harvard’s campus culture. At this point in my life, the focus on finance, government, economics and the excitement of a true Winter Christmas experience pushed me East. Stanford got the cut.
Finally, Penn (Huntsman) and Harvard. I think the Huntsman program is incredible - it would have allowed me to continue to develop my French with a very specific focus on linguistic development, study at Wharton (the world’s best undergraduate business school) and also pursue a BA in international studies. It also offered an intimate class of Huntsman peers who benefit from fantastic advising, support and a wonderful community which is disproportionately international compared to the rest of Penn. I found the preview days wonderful and loved my peers and Philadelphia. Huntsman is roughly as difficult to get into as HYPSM although admission rates aren’t disclosed.
Ultimately, I decided that while I liked Huntsman, I would rather be in an environment like Harvard where every student is admitted equal into the same undergraduate program. Being in a community of 1600 vibrant, talented, passionate individuals to me sounded more exciting than being in a community of 50 in the Huntsman tucked away as a part of Penn. Penn is wonderful as well but typically for dual admits between Harvard and Penn, roughly 4 choose Harvard for every 1 that chooses Penn. I believe strongly that you’re a function of those you surround yourself with and Harvard does a fantastic job of recruiting a diverse class of leaders within a wide variety of fields and being a part of that ecosystem was simply too exciting to turn down.
(http://www.parchment.com/c/college/tools/college-cross-admit-comparison.php?compare=Harvard&with=University+of+Pennsylvania).
Harvard ultimately won for me because I loved the Applied Mathematics program (https://www.seas.harvard.edu/programs/applied-mathematics) which offered a mathematically rigorous lens through which I could study economics. It also offered arguably the strongest on-campus recruiting process (http://ocs.fas.harvard.edu). I was also very excited to leverage Harvard’s wonderful economics research opportunities. For my broad interests in economics, finance, government and politics, I felt I had found my home.
I have always been very happy with my choice! (Harvard '16 A.B./S.M. 
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