HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

It wasn't, but it is now.
How is that better?

Isn't it obvious? There are no quick transfer/split/merge buttons, no healing for split heroes/faded castles, and no option to launch the game in an arbitrary resolution, only 800*600.
And no passwords for saves.
That's what makes it better! Because none of that exists!

The advantages are clear. Only a blind person wouldn't see them.