Nokia Lumia 1020 - What is the difference between the displays of my phone and Nokia Lumia 920?

Your phone has an AMOLED display whereas Nokia Lumia 920 has an LCD display. The display size is the same. An AMOLED display offers very high contrast, wide color range, excellent viewing angle, and fast response. Additionally, your phone introduces new features like Nokia Glance Screen and double-tap to wake the phone. This means that you have, for example, your clock visible on the screen and you don’t need to switch on the screen to see it.  Double-tap lets you wake up the phone by just tapping the display twice.