The Assassin in is FfH2 (and was before AoI was made), but it isn't really the same unit. It doesn't have the bonus versus melee units (which aren't as common in normal FfH anyway, sine it has extra classes like Beast, disciple, and arcane), but starts with the marksman promotion (which makes it attack the weakest unit in the stack rather than the strongest). It also has poison damage, which gives living units it attacks a chance of getting the poisoned promotion, weakening it (and causing negative healing before that was made impossible). It upgrades to a shadow, which is even stronger. I forget whether assassins may be used like spies, but I know shadows can be.
Actuay, the Amurites don't have an Assassin unit it is replaced by their unique unit, the Chanter. The chanter is just like an assassin (and uses the AoI assassin graphics), but starts with channeling I and Dimensional I. This lets Chanters teleport themselves directly back to your capital. Channeling I also give it a slight chance of gaining xp each turn without need for combat. The Chanter unit is kinda irrelevant though,since the Amurite Hero, Govannon, has the ability to teach other living, non-animal, non-disciple units several first level spells (i.e., give them channeling I and the first level of dimentional, death, chaos, or body)