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As Devils Advocate has noted, there are differences and similarities. And as Leo has noted, a 4500 supervisor is a point of comparison (a rather important one). Choice of line cards, in the 4500 series, also are a point of comparison.
A couple of major differences, though, are due to their basic architectures. The 4500, in the smaller chassis, like the 4503, do not support sup redundancy, while once you stack 3850s, you have "sup" redundancy.
The 4500 sup provides a real fabric between line cards, while the 3850 provides a "special" stack ring between stack members.
IMO, the 4500 is a much more stable (mature) product, also sold as "carrier grade", while the 3850 (still rather new!) are more suited as edge switches.
Besides "paper" features, much would depend on what role you wanted to use either switch in, and how critical such usage was to your business. For example, I would be a bit nervous using a 3850 for a core or distribution L3 role, but might lean toward using a 3850 as a high performance/capacity L2 user edge.
