I have had this argument with friends and family many times. 1080p vs 720p. I personally can easily see the difference between 1080p and 720p, whether it is on a 60hz, 120hz, or 240 hz TV it makes not difference, I can still tell the difference. I also tell the difference during very heavy actions scenes between all of the above hertz ratings. During regular scenes in a movie, there is not a noticeable difference between 120hz and 240hz for me. Every person is different in what they see and hear.
My sister, back in the day, could not tell the difference between a properly connected (component) DVD movie and a movie on VCR hooked up with a coax connection.
It all depends on the person and their attention to detail. Most people will see a difference between 720p and 1080p on anything larger than a 27 inch wide screen TV. The average consumer will also not be able to see the difference between 5,000:1 and 30,000:1 contrast ratio in a non LED LCD TV. They also will not see a difference between 60hz, 120hz or 240hz unless it is blatently advertised to have a better refresh rate. To most consumers the HZ and contrast ratio are just bells and whistles and technical jargon. That is why they are still able to sell boat loads of 40inch 1080p LCD with 3,000:1 native contrast ratio running at 60hz.