When you set the compression level to Fast, the compression ratio is lower, resulting in an increase in the speed of the rendering of the UI. This is recommended when the computer that you are connecting remotely to is in the same LAN as the computer you are connecting from.
When you set the compression level to Best, the compression ratio is higher, resulting in a decrease in the consumption of the bandwidth. However, the rendering of the UI will be comparatively slower. This setting is recommended when the computer that you are connecting to remotely is at a different geographical location.