It sounds like you both are top students and will do fine in the end.
I mostly want to echo a comment above. “Prestige” is one factor in the college selection process. And it’s one that, to me anyway, gets way, way overemphasized, disturbingly so. Yes, Harvard, Yale, and Princeton are great schools. So are many, many more. Do you think that engaged, hardworking students at Oberlin aren’t getting a similar education? Harvard, Dartmouth, Penn, Stanford, and MIT are so different in so many ways. Dartmouth is a midsize school in a small New England town, in the mountains, not close to very much except some small Vermont towns. Penn is IN Philadelphia. Besides a small, nice strip of campus, you are in a gritty, industrial East Coast megapolis. Both are wonderful. Besides prestige, I would submit that they are the perfect fit for very, very few students. Yet many apply to all the Ivies, so apply to both of these.
If you and your friend take a balanced approach to choosing a college, where you weigh many factors, and try to find a good fit for yourselves, as individuals, I think you will come up with different lists. If you and your friend understand that it’s HOW you go to school not WHERE you go to school that is most important, again you will come of with lists of schools that are good places for YOU, where you can afford and where you will grow and thrive. That school might be ranked #3 or #23 or #43 or wherever. You have both done well academically in the same school and have done lots of outside-of-school stuff together. That does not mean you would not find Penn exciting and your friend Dartmouth enchanting, or vice versa.
If none of that makes sense, you could get a solid list of the TOP 20, put the names in a hat, and then take turns drawing them out until you each have ten schools where you could apply without overlap. That is just about the same logic as applying HYPSM or All Ivies.
(Sorry, just be stark to make a point. Go find the place you love, Work hard. Embrace opportunities. Engage with the amazing people around you. Treat everyone with respect and dignity. You both will do great. And, seriously, don’t do the hat thing.) Good luck!