Using a navigation drawer that is off-screen, and will slide in when a user clicks the 'hamburger' icon, should that drawer push all the content to the right, or be an overlay on top of the content.
What are the benefits or cons to doing either?
Push content to the right if you want to suggest that the contents of the drawer are conceptually distinct from, or more important (at the moment the drawer is being displayed) than, the main content.
Pushing content to the right, and potentially off the screen, suggests that the main content isn't needed, or has been put on hold, when you're working with the drawer. The effect gets much stronger if you add a semitransparent overlay onto the main content to visually separate the two areas.
An overlay that leaves the content in place (e.g. the Evernote Web Clipper) doesn't reduce the importance of the main content. The downside, of course, is that the contents of the drawer have to compete more with the main content for attention.
In Apples user interface guidelines about using transitions they recommend you to use full screen animations in an Ipad app sparingly because it could make the interface feel messy. That is something to take into consideration.