When you play a 1080p Blu-ray on a 4K display TV, the image is upscaled to fit the higher resolution of the TV. The quality of the upscaling can affect the picture quality of the 1080p content on the 4K TV. Additionally, the quality of the video itself can also impact how it looks on a 4K display. If the source material is of poor quality, it may not look as good on a 4K TV as it would on a full HD display TV.
It's also worth noting that the perception of picture quality can vary from person to person. Some people may notice a difference in picture quality between 1080p content on a 4K display TV compared to a full HD display TV, while others may not notice much of a difference at all. The size of the TV and the distance from which you are viewing it can also impact how the picture quality is perceived.
Overall, while 1080p content may not look as good on a 4K display TV as it would on a full HD display TV, the difference in picture quality can vary depending on several factors, including the quality of the upscaling and the source material.