Hello gannelx. No, I am not a CS student at CMU, just a parent of students who applied to CMU and an alumnus who was there at CMU at the birth of SCS. I have stayed active in the CMU community over the years by serving on various alumni organizations.
Let me address what I see as some of the questions / issues raised by you.
First, as to being an entrepreneur, you donāt really need either of these places to do that, right? There are countless examples of wildly successful entrepreneurs who went to little or no college. Having said that, if you are also interested in getting the best possible advanced education, the CMU CS community is particularly well connected at this time with early stage and established computing based companies. If you end up at SCS you will be pretty much assured of having many opportunities to develop and implement business ideas. Or, maybe even better for you in the long term, you will be able to work in a well managed CS based company, learn some things about starting and growing a business, meet people you would be interested in working with, then striking out on your own. I am not nearly as familiar with Columbia, but I suspect you are right that NY offers certain advantages based on sheer size for a young person interested in starting his/her own company. But the action in CS really is in the SF area of CA and maybe Seattle now, and the link between CMU and these companies is very strong and clear at this time.
From the people I know in the CMU CS community, it is a very intense environment, but if you are good enough to be admitted, then you will be good enough to navigate thought the curriculum and still have opportunities to branch out in ways that are interesting to you, especially if you have the flexibility to spend 5 years to do it. The important thing, it seems to me, is that when you leave CMU you will have this incredibly strong credential which immediately tells the world that you know what the heck you are doing and that you are able to work hard enough to get what you want.
Let me interject a side thought at this point. If you are interested in law, the main things are grades and LSATS. If you go to CMU, thereās no reason why you shouldnāt do well on the LSATās, but it will be very difficult to keep grades up to the 3.5 - 3.8 range you will need for top law school admission. Itās unfortunate, but thatās just the way it is in law school admissions these days. Same with med school. Itās grades and board scores mostly. So thereās something to think about.
From what I know, Columbia University has a good and improving CS department inside of the Fu School of Engineering. With a little research, you can find out how CS at Columbia is strong vs CMU. Is it a theoretical school? Do they emphasize programming? How does it contrast with CMU?
Hereās the big difference between CMU and Columbia. Columbia has the best humanities curriculum, professors, and classesābreadth and depthāto be found in the world. They are right up there with Harvard, Penn, Yale, etc. And as you know, Columbia has the core, which will may be an advantage or drawback depending on your interests and point of view. CMU has good humanities, but not at the level of Columbia. So if it is your interest to study great novels with a world reknown professor, it would be harder to do for sure at CMU than Columbia. Donāt forget, however, that CMU ,with its College of Fine Arts, essentially has a conservatory inside the University. This is particularly true with its theater programs.
Hereās where I will venture an opinion. Humanities and CS are fundamentally different in their approach to their disciplines. Humanities are by their nature without a precise answer or end, while CS is a āhard scienceā with an empirical approach and definite results and answers. So you are talking about two disciplines which are cognitively at odds with each other. So if you went to Columbia, with a double major in, say, CS and Philosophy, you would have to deal with this issue inside your own mind. Maybe this is what you want?
I donāt know enough about you to make a definite recommendation to you about what you should do, but I hope I have laid out some thoughts that gets you going, and maybe others will weigh in. Of course, you will seek advice from parents, counselors, respected friends as well.
Hereās a thought. CMU CS is now one of the most competitive admissions in the world. I would argue that it is even more competitive than the percentages would indicate because there is self selection going on as well. CMU values interest highly. ED is a great way to demonstrate interest. If your qualifications are as good as you suggest, might it be a good thing to apply CMU ED in SCS and Columbia RD?
Good luck to you.
. The problem is I cannot decide which of the 2 to put as my early decision. I definitely want to major in computer science but am not sure whether I would be able to cope with the curriculum at Carnegie Mellon (pretty rigorous) 
. Iām not saying that Columbia is less rigorous but I fear that I shanāt be able to cope up with CMUā¦ The problem is exacerbated by the fact that I would like to double major in the humanities as well. I am not sure what I will be doing after I graduate (grad school in CS or Law or BME or job). I am leaning towards Columbia but hesitate for Carnegie Mellon is supposed to be one of the top computer science schools. Will I be disadvantaged by my choice (assuming I get in 