The difference of offline play in Heroes II and Heroes III.

But there is also a building that is missing in the third game – the Sphinx.

Actually, the Sphinx is in the third game (In the Wake of Gods, The Restoration of Erathia), but it behaves completely differently.
In the second game, as far as I remember, the hero who decides to visit it gets eaten! :)
In the third game, it's simpler – a curse, like a ban on teleports :), or money will be deducted – all of this lasts only a few days and then passes.
So, not answering the Sphinx's question in the second game is much more dangerous than in the third game.