An electronic device may have a camera and a display. The display may be configured to display virtual reality content for a user in which no real-world content from the camera is displayed or mixed reality content in which a combination of real-world content from the camera and overlaid virtual reality content is displayed. Control circuitry in the device may adjust the display and camera while transitioning between virtual reality and mixed reality modes. The control circuitry may reconfigure the camera to exhibit a desired frame rate immediately upon transitioning from virtual reality mode to mixed reality mode. Transitions between modes may be accompanied by smooth transitions between frame rates to avoid visible artifacts on the display. The camera frame rate may be synchronized to the display frame rate for at least part of the transition between the virtual reality and mixed reality modes.