Hi Stefan.

@You : "... think the trick with rendering larger images..."

Yes, undoubtedly in this way you can get a less pixelated final image but at a cost of much more render time.
I you render a frame at 4K resolution and then you perform a scale down to a FullHD res, for sure you
will get a better looking image but the initial render time is increased by 4x!

If the time is a key, this method is not good at all.

You can get better results in terms of time and also, is some circumstances, in terms of quality,
if you use a software like Affinity Photo or others to apply a post process effect to the rendered images.

Furthermore...I've tried also the (now official) "Denoising" feature of Blender 2.79 and in many circumstances it can offer great improvement to the final render at a cost of a small fraction of increased time (about 20%).

Ciao!