This video shows a comparison of the performance Lumia 1520, 925 and 620. The video compares the start-up time for built-in apps (same for all devices), third party apps (Lumia 1520 fastest, followed by Lumia 925, with Lumia 625 slowest), and boot-up time.
The key point from the video is that while Windows Phone performance is a little better on the Lumia 1520, powered by the Snapdragon 800, the difference is not as big as you might expect. This reflects the fact that Windows Phone is arguably the most efficient of the major smartphone platforms, able to run smoothly on a wide range of hardware.
The Lumia 1520 has a Quad-core 2.2GHz processor (2GB RAM), the Lumia 925 has a Dual-core 1.5GHz Dual core processor (1GB RAM), and the Lumia 620 has a Dual-core 1GHz processor (512MB RAM).