1080p on a 70 inch monitor is going to look worse than 1080p on a 24in one. that's just a factor of pixel density. Though hopefully you're on a 4k screen if over 40". That would mitigate that issue significantly.
That's what i think he's getting at, not necessarily resolution. Cuz you can render at 1080p on a 4k screen and it will look better due to the pixel density than a 1080p image on a 1080p screen of the same physical dimensions. One just has less pixels for the same area
edit: or maybe he's just referencing how often the geometry will be simplified, as will shader effects and texture complexity to deal with the more restrictive console hardware. Or the fact that if you're limited to 1080p, displaying on a large tv that is native 4k will cause scaling of the image using the tv's hardware ...which depending on how expensive your tv is, might not be that great. So you get noticeable scaling artifacts, while a smaller screen makes those less visible or unnecessary due to the native resolution being 1080p.