How they break down
Unlike PMD, Checkstyle can check for Javadoc commenting; however, PMD offers a useful feature called CPD, which checks for copy pasting of code. With PMD, the errors I found most frequently were unused imports, unused private variables, and the occasional duplicate literal. Checkstyle found many more errors. Along with detecting missing Javadoc comments, it caught line width beyond 80 characters, variable names not following conventions, and tab usage instead of spaces, among other things. Both tools give you the option of creating your own rules.
If you want to adopt one of these for your organization, Checkstyle seems a better choice: It checks for most things that company code conventions expect. PMD is a good option if enhancing code quality is your main goal. But if you want to go further and actually have the tool fix your code for you, check out Jalopy.
Jalopy is an easily configurable source code formatter that can detect, and fix, a number of code convention flaws that might appear in Java code. Jalopy is more of a code fixer than a code checker.