Multiplayer and the number of planets in the galaxy are scaled entirely differently. Multiplayer and the number of starting home planets you choose are scaled exactly the same. Just to be clear there.
In terms of multiplayer/multi-planet-starts, it's mainly that the AI gets more of everything, and gets 2x the number of human players/starting-home-planets in terms of waves. Also there are some other things in there, like extra resources getting seeded into the map when there are multiple players, and the AI is implicitly a bit harder because of your increased surface area for your planets (but also implicitly a bit easier since ALL your home planets have to be destroyed before you lose -- well, in multiplayer, not multi-planet starts).
In terms of the size of the galaxy, if you play 10-15 planets it's brutal hard due to lack of knowledge, etc. Anywhere up to 80 planets uses pretty much the same percentage of mark III/IV worlds on the map, and so depending on the map type the higher-planet-count maps might be easier or harder. Harder, because you have further to travel. Easier, because there is less density of stuff, and thus you can get goodies without tripping over quite so many major weapons of the AI. And there's knowledge galore.
On higher than 80 planets, it uses a slightly larger percentage of III/IV planets, so that takes another jump in difficulty, but again since there is so much more room it tends to work out pretty evenly, I'd expect. The game was designed around 80 planets, but most people seem to like 40, 60, 80, or 120 planets. I think it's reasonably the same at any of those, with the biggest thing that changes being game length. Assuming you're not going for a completionist strategy, and are using sensible strategies for planet hopping, etc.
I didn't say identical, though: just within a standard deviation either direction until you get below 20 planets, in my opinion.