Stanford University Campus OvalVia Wikimedia CommonsStudents walk around the Stanford Main Quad.

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What the growing rivalry between the schools might boil down to, though, is a stark difference in educational philosophy.
While Stanford is certainly the hottest school in the country right now — with its engineering prowess leading to a near-domination of Silicon Valley — Harvard is playing catch up, The Crimson reports, and "is positioning itself to be the leader in education and research in the 21st century."
The difference between the two educational juggernauts is fairly simple — Harvard has a focus on intellectual growth, while Stanford seeks to give its students more practical knowledge. As Meg P. Bernhard at The Crimson writes:
Stanford's objective to "qualify its students for personal success, and direct usefulness in life," as stated in its founding grant, differs greatly than that of Harvard, which according to University literature, focuses primarily on the advancement of knowledge.
... Harvard focuses not so much on the application of education, but, as Harvard President Drew G. Faust wrote in an official capital campaign message, on the discovery of knowledge and the education of future leaders. The University remains true to its founding charter from 1650, part of which emphasizes the "advancement and education of youth in all manner of good literature, arts, and sciences."
A Stanford computer science major offers a more real-life example — "We see Harvard as more focused on theory, the softer side ... Even in computer science, there's a lot more focus on how you do things as opposed to Stanford, which focuses a lot more on the practicality," he told The Crimson.
This philosophical difference could be a reason why many Stanford students are finding early prominence in Silicon Valley. According to The Crimson, "at Stanford, the culture of looking forward is amplified by the successes of current students, not just graduates."
As one Stanford history professor told The Crimson, "Every time a Stanford student reads that someone he met at a frat party just sold a startup for $1 million—and that happens a lot here—it dribbles a few more toxic drops into the water ... It shapes students' aspirations."