The main factor when it comes to promotions seems to be the number of aliens a soldier has killed. Does it matter what kind of alien is killed? Does a strong alien give more experience than a weak one, or are all aliens equal?
jprete pointed out that there is the file DefaultGameCore.ini which lists all relevant stats of the aliens (as well as a lot of other gameplay stats). The alien data does not contain anything which looks like an exp stat. This heavily hints that all aliens do indeed give the same amount of exp.