A Full HD is a screen is of 1920×1080 pixles. This can accept and play images that have been scaled up to 1080 p with progressive scanning.
A HD Ready screen on the other hand has a native resolution of 1366×768 pixels and can display images with upto 720 p resolutions. Though it will also accept a 1080 p image, this will be down scaled to match the screen’s parameters.
A Full HD system will make sense only if you have a screen size of 42 inches or more. Less than that, a HD Ready system is more that ample.