We refer to Confluence 5.9 and the projectdoc Toolbox 1.10 for our discussion.
Please bear in mind that projectdoc is our product - so there we are certainly biased in favour for document properties.
Nonetheless we hope that our discussion is fair.
If you think this is not the case, especially if you feel we are lacking knowledge of features in favour of page properties, please give us a shout! We will check and adjust your issue with our presentation.
Summary
Page properties are easy to use, but up to version 5.7 of Confluence provide limited capabilities to select and display the properties. While document properties provide some additional features, people my consider specifying the where clause to constrain the search result as complicated.
If page properties is providing all you'll ever ask for, you should stay with it: it is free and is part of every Confluence installation.
If you are asking for more and paying for additional features that make you more productive is not a problem for you, check out document properties.
The following table lists features that are related to one of the macros discussed, but are implemented by different macros. In this case the macro providing the feature is listed. No extra cost is involved to use the mentioned macros, since all these macros are either part of Confluence or the projectdoc Toolbox Add-on.