Hey SwissTom,
cool question and generally the answer would be on the left hand side. But it depends on whether they're using the northerly or southerly runways. 80%+ of the time it's the northerly, so after take off downtown and the Burj Khalifa are visible to the left. If you're really lucky you get a departure with a left turn and you circle downtown counter clockwise.
Coming into DXB it's harder. If the southerly runway is in use then the right hand side will afford you good views, but if it is the northerly you might not see it at all, though I still think your best bet is the right hand side as most approaches fly a downwind to the north-east of the airport, so you'd see the Burj Khalifa and nearer to you the DXB Airport from somewhere around 5000-6000 ft.
However be aware of the timings of your flights as well. It's very difficult to get a decent photo at night, especially from a phone, due to the glare of cabin lights and screens in the window, poor performance of the cameras in low light and the vibrations of the aircraft preventing a steady photo at the required longer exposure time.