Look at the example, if dnd-draggable set to true ng-click event never fired.
http://embed.plnkr.co/w5vP9BK3xVztYhVBe2OI/preview
You need to implement something like dnd-drag-delay option or dnd-drag-delta to start dragging after a few ms after onmousedown or after cursor were moved a few pixels away from start point with button hold pressed. Something similar is done in angular-ui-tree https://github.com/angular-ui-tree/angular-ui-tree