The major differences at an Ivy will be the famousness of your professors, the quality, quantity and accessibility of research on campus, the resources the university has, the recruitment opportunities, and the network you join by having gone to an Ivy. Additionally, students at Ivies all tend to be pretty exceptional (though that is of course not true of every Ivy student) whereas at a big state school you will find a much greater degree of differentiation between the quality of the top of the class and the quality of the bottom of the class. Essentially, the average student at an Ivy not only has better SAT/GPA/Class Rank metrics than the average student at a flagship state school, but they also had to have an extra ‘wow’ factor that allowed them to stand out for the sub-10% admissions rates common to most ivies (Harvard, Columbia, Yale, Princeton, Brown and Penn). So you end up being part of a community of highly concentrated talent and brain power that isn’t possible at a state school because state schools serve a very different (and probably more important) purpose of educating the American public broadly.
There is variation among the ivies, as has been mentioned. Some ivies supposedly have a more graduate-focused feel to them like Columbia while others like Dartmouth are purportedly more undergrad focused. But no matter which Ivy you attend, you will have access to a disproportionate number of the greatest professors in the world, the brightest minds of your generation, easier access to the most coveted jobs, and of course bragging rights. Furthermore, your network will be more national and international than it would be a big state school. For example, over 50% of Michigan undergraduate population comes from the state of Michigan. In contrast, only 18% of Penn students comes from Pennsylvania and only about 20% of Columbia’s students come from New York. And on the international front, only 4% of Michigan students are International students compared to Penn’s 11% and Columbia’s 17% international populations.
The ivies are also just smaller than big state schools and that can have a huge impact on access to study space, classes, professors, job/recruitment opportunities, chances at becoming a leader in the most prestigious undergraduate organizations, housing options, and much more. For example, UVa’s undergraduate population is a full 44% larger than Penn’s. And UVa’s undergrad enrollment is about 57% larger than Columbia/Barnard. Furthermore Michigan’s is a whopping 144% larger than Penn’s undergrad enrollment (even inclusive of part time students and non traditional programs like LPS). And Michigan is about 168% larger than Columbia/Barnard (also inclusive of part time students and non-traditional students). That leads to enormous differences in the student experience.
The vibe is also very different at a state school than at an Ivy, for better or worse. At Michigan you’ll have huge sports fans that really care about when they win or lose. At a place like Penn, the level of interest in athletics is much lower; students really only care if we beat Princeton. And at Princeton, students only care if they beat Harvard and Yale. And at Yale they only care if they beat Harvard. And at Harvard, they don’t really care who they beat but they enjoy reminding yalies of their inferiority 
. And at a place like Columbia, sports don’t really matter at all. Furthermore, most flagship state schools are not in big, urban environments whereas most ivies (Harvard, Penn, Yale, Columbia, and Brown) are all in cities of varying fun and quality. It would literally be impossible to compare a place like Ann Arbor to cities like Philly, Boston and New York- the sheer size of those three cities and the opportunities for cultural enrichment, internships, access to each other as well as other major and minor cities like DC and Baltimore, access to important speakers who are just passing through the city and choose to make a speech-- it’s all simply not replicable outside of these extremely populous metropolitan areas.
There is also going to be some elitism at the ivies that you won’t find at state schools. The NYT just pointed out that there are more students from the top income bracket at schools like Dartmouth, Yale, Princeton, and Penn than there are from the bottom 60%. At the ivies, you’ll be in very close proximity to the heirs and heiresses of massive fortunes and hyper famous political families. For example, at Penn’s most recent commencement, both Joe Biden and Donald Trump were in the audience because Biden’s granddaughter and Trump’s daughter were both graduating from Penn’s College of Arts and Sciences. I believe Caroline Kennedy’s son and Senator Rob Portman’s son both graduated from Yale in 2015. Emma Watson graduated from Brown with Kevin Bacon’s daughter. Put simply, it can be a little jarring for an average, middle class kid because the ivies are pretty small and attract this disproportionate number of wealthy/famous students that you inevitably interact with on a regular basis. But that also leads to an impossibly strong and varied network after you graduate.
Finally, after graduation, when you’ve graduated from an Ivy you’re part of the broad network of ivy alums. Ivy alums consistently hold ivy-only networking events and share information about job opportunities with one another. It’s easier to navigate the most elite professions when you’ve gone to an ivy because you’re entrenched in a community that, for better or worse, has a disproportionately strong influence on those fields. And there are social benefits too: ivy only mixers, access to the Alumni Clubs in NYC and around the world, reciprocal benefits at the other Ivy clubs, etc. etc. etc.
But while the ivies do provide a particularly unique experience, it’s also important to keep in mind that you can be extremely successful and fulfilled at a state school as well. Numerous studies have shown that if you are qualified to get into an ivy but you choose to go to a state school, you will still be extremely successful because most opportunities in life are created by hard workers who put their noses to the grindstone and make something of themselves. Sure, if you want to break into the most elite job markets right out of undergrad it will be easier to do from an ivy; but there are a million ways to lead a good life and where you go to college doesn’t define you by any means. America is privileged to have some of the ABSOLUTE best state schools in the world (Berkeley, Michigan, UVa, William and Mary all come to mind), and bright, talented students to fill them. Go to the schools you can afford and that will make you happy- those are the best kinds of colleges to attend.
