4k is literally a resolution, usually 3840x2160 or something around that. 1080p is another resolution, usually 1920x1080. These are never comparable.
You would be right if lossy compression wasn’t a thing. But it is, and it’s getting used a lot.
“4k” can very much be worse than 1080p if it’s compressed in a way that erases more details. That’s what people are complaining about with streaming services and YouTube - the resolution numbers don’t mean shit, and quality at a given “resolution” has been degraded more and more over time.