In the end I'll be shrinking my vids down to 1080 but was wondering if 4K or 2.7K was less noisy than the other?

I wonder why you think there will be a difference? It is the same sensor, using less pixels.
I suppose if you have fewer pixels, there must be less noise overall, but  it will be the same noise to pixel ratio.
Then again, how are you going to view the image?
If you have a 4K screen, then 2.7K data will be interpolated (guessed), to fit the pixels on the 4K screen. This is always worse than 2.7K on a 2.7K screen.
The same issue applies when you play 4K on a 2.7K screen.
In both cases, noise and artefacts will be more noticeable.
Have you considered the colour gamut? If a colour level cannot be displayed because of the monitor, perhaps the larger step between levels looks like noise?
Have you recorded at the optimum exposure? This can make a large difference to the signal to noise ratio.
There are many reasons for the appearance of noise, including confusing grain for noise.
For best effect, the monitor/screen must be at the same resolution as the image/video and be at least as good as the other factors that make up the image. Bit depth, gamut, frame rate... and others.