4k material in a 1080p timeline that is not scaled to 200% or greater will be less sharp than the original 4k image scaled to the same amount. A 3840 x 2160 image contains 8.3 million pixels. A 1920 x 1080 timeline contains 2.1 million pixels.
At 100% Scale: You are forcing 8.3 million pixels of data into a 2.1 million pixel container. FCP must discard or average 75% of the source data. You are technically "seeing" the whole image, but you are absolutely not seeing "all available source pixels."
Consider your 4k source material in a 4k timeline, and also in a 1080p timeline. In the Video Inspector under "Transform" if you do "Scale (All)" for each timeline such that the *visual* magnification is equal for both 4k and 1080p images, and provided the 1080p scaling is 200% or greater, they should both look equally sharp in the FCP viewer and if both were exported at 1080p.
A 4k image in a 1080p timeline retains the full resolution capability -- but only if scaled to 200% or greater. If you put 4k in a 1080p timeline and only occasionally punch in, the non-scaled portions may look less sharp than 4k in a 4k timeline, if viewed on a 4k-6k monitor.
Re "can I instead create a 4K timeline, drop in 4K footage and crop in on it as needed, render, and export at 1080 for the same resolution as if I did a 1080 timeline?" The answer is yes. This can cost some performance as the render cache will then be 4k not 1080, but there are some cases it could help quality.
However, there is another mechanism that may in some cases soften 1080 exports from 4k originals. As an optimization, FCP may sometimes attempt to export from render cache, not from the original media. If your timeline is 1080p, so is the render cache. So in that case, it's transcoding 1080p to 1080p. By contrast if 4k originals are in a 4k timeline, if FCP uses the render cache export optimization, it's transcoding 4k to 1080p which will be sharper. I'm not sure the conditions under which that happens.
FCP uses several different export paths:
- Start with original media, apply timeline effects, export from originals via transcoding.
- Start with render cache (Fx already applied), export from render cache via transcoding. That is faster since the Fx are already applied to cache.
- If final export format matches the render cache format (e.g, 4k ProRes 422 render cache, and exporting to 4k ProRes 422) it will not encode anything, but concatenate the render cache segments and copy those to the output file. That is extremely fast.