Young product managers at Google or Microsoft don't get the opportunity to work on big problems. The few young people I've met tend to lack the macro thinking on what makes a product successful. Why talking to users is so important. Why defining a problem is so important. Why retention is more important than growth. Why cohorts are so important and why analytics can be misleading.
With young engineers, they tend to lack the understanding on why striving for simplicity is important. Why thinking in iterations is important. Why writing tests are important. Why the best engineering in the world can't save a product that doesn't solve real problems.
Big companies do teach you these things, but not at the pace of a real startup.