400-level versus 500-level Real Analysis

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I'm preparing to start a year-long sequence of 400-level real analysis using Rudin's Principles of Mathematical Analysis 3E in my second undergrad year, and my advisor recommends I take the graduate-level sequence the following year through Real Analysis by Stein and Shakarchi. Since both of them seem to cover the same field of mathematics I was wondering what general topics I might expect to see in the 500-level course that might not be covered (or covered in as much depth) in the undergraduate course?

 

[Vanadium 50]

What does the course syllabus say? That's definitive - not some people on the internet.