Downscale to "native" look
Your understanding of sampling seems to be a bit off.  When downsampling from a UHD stream you don't have more information than a native 1080p sensor capturing it, you have less.  When the 1080p sensor is capturing video, it has near infinite points and photons it can capture as it is looking at a real life source.  Each photosite captures exactly what photons hit it (within the margin of error of the photosite anyway).

With downscaling, you have a much, much smaller amount of input.  All you have is the samples available and you don't know exactly where within the pixel they came from.  If the sample is an exact multiple, then it is still possible to make an exact 1:1 mapping by combining a group of pixels in to the only pixels they impact, however if you do not have an evenly divisible number of pixels, then you can't determine the exact impact of your new set of pixels from your old and you have to apply some type of imperfect translation between them.  

This imperfect translation will produce less positionally accurate information, but also can have other advantages.  One advantage of downsampling is the reduction of noise.  Since noise is random, averaging multiple samples together will generally reduce noise when all other factors are equal.  It's ideal for this to be done at an evenly divisible interval to avoid needing to translate data between pixels, but the advantage is still seen with any downscale.

Getting back to your question however, unless you are shooting an even multiple of 1080p or choose to crop your sensor input to an even multiple of 1080p, you will have some type of translation of pixels.  If you want the most "natural" look, I would encourage using a resolution and aspect that allows you to directly map pixels.