I bought the more expensive version from Steam (sorry I don't remember the name - only that there were two versions at two different prices, one with extra content). Are the two versions compatible in multiplayer? Can I play against an opponent who does not have the expensive version and instead bought the cheaper one?

Yes, there should be no problem playing against players on Steam with varying versions. The more expensive edition gives a new but purely cosmetic skin for a playable base game faction/race.