1080p and 720p settings have substantially different fields of view

[ras07]

720p has a much wider viewing angle than 1080p does (roughly 1.5x the field of view). Interestingly, when you start at 720p and step the resolution up incrementally (say by adding 16 to the width and 9 to the height, to maintain the aspect ratio) the field of view stays exactly the same, until you get to 1504x846, when it suddenly jumps to the "zoomed in" field of view that you see with 1920x1080.

Is there a way to get the same wide-angle field of view at 1080p that you get at 720p? I know you can narrow the field of view with the Sensor Region settings, but you can't widen it.

[roberttidey]

This is a characteristic of how the camera sensor is dealt with. The FOV is also different for V1 and V2 cameras as they have different native resolutions.

Check out https://picamera.readthedocs.io/en/release-1.13/fov.html#sensor-modes for a good explanation of how FOV varies with resolution.