xaritas has hit the nail on the head with the key differences...
As I see it, Django CMS's philosophy is to pass on as much flexibility as possible to the editor in terms of page layout. Wagtail takes a more 'prescriptive' approach where the page content has to fit a particular data model (such as an event page that has a start/end date, list of speakers and so on) - which means a little less freedom for editors, but on the flipside, it gives the site creator a lot more control over page layout and design, makes it easier to repurpose that data, and goes a long way to making the editor UI friendlier (since it's a case of 'fill in the gaps' rather than a blank canvas).
As I see it, Django CMS's philosophy is to pass on as much flexibility as possible to the editor in terms of page layout. Wagtail takes a more 'prescriptive' approach where the page content has to fit a particular data model (such as an event page that has a start/end date, list of speakers and so on) - which means a little less freedom for editors, but on the flipside, it gives the site creator a lot more control over page layout and design, makes it easier to repurpose that data, and goes a long way to making the editor UI friendlier (since it's a case of 'fill in the gaps' rather than a blank canvas).