POM or Displacement with tessellation

What is better for performance to make a towel or carpet, etc to ArchViz quality?

Don’t think you need any, may look a bit coarse. A high res diffuse and normal map should do, otherwise you may check epic’s own Realistic rendering apartment level where they use an actual mesh for a furry carpet.

POM is best pick for a flat carpet, lying on the floor. For towel hanging somewhere, you should probably only use ordinary material with some fresnel effects to simulate cloth.