I can't say too much about Harvard's EAS program, but I can say this for Princeton's. I am NOT an EAS major in any way, but I have taken Chinese courses in the department. While rigorous, I couldn't believe how phenomenal the program was; in just one year, I've learned about ten times as much as I did in 3 years in high school. I won't continue with a page of praising, but I intended to just stop at second year (to pass the language requirement). However, the department impressed me so much that I am continuing chinese (no longer for any distribution requirement). I have several friends who have also recommended non-language EAS courses.
To attempt a comparison to Harvard, I did a quick google and found this article. It's a bit outdated (like 10 years old), so I can't expect to make a fair argument from it, but nonetheless, here it is: Ranking the Concentrations | FM | The Harvard Crimson