With a beam expander your beam "dot" will be smaller (more concentrated),
so it will appear brighter,how much, will depend on the divergence of your laser to start with and the distance.
With 2X the power the perceived brightness will only appear .5X brighter (4X power=2X perceived brightness)
It's pretty much a toss-up IMHO.
Trial and error would be the sure way to tell.
As wbayw stated the air conditions (temp./humidity) will play a big part in the difference.
Maybe some of the math wizards here, could figure this out mathematically.
If you have a lot of power but bad divergence you will see the dot far away, but it will be huge, so it wouldn't be so bright. If you have good divergence with less power you will see the dot far away and it will be tiny and bright. Divergence is more important than power I think.
It depend what do you want to see? Large dot, or tiny but brighter dot?
since the surface of the dot is a squared function of the divergence (and dot brigthness an inverse function of dot surface) , i think you need 4x more power to achieve the same brighteness increase than /2 divergence.
and the rayleigh diffusion is function of beam intensity too...
so as we thought this is from far better to increase beam diameter and reduce the divergence than increase power.