What's amazing about the Tornatore collaborations is simply how good they are. Some directors like Leone and Tornatore really seem to have consistently received the very best of Morricone.
There are several "kinds" of Morricone. The three main ones, to me are:
1 - The music he does for Tornatore is Morricone at his most "regular". The tunes are romantic and often powerful, the arrangements are utterly traditional: this is regular orchestral music. That's the stuff he does kind of effortlessly I think since he's often turning to these kinds of compositions even for others (The Professional, 1900...). Some of these musics are corny and some of these are great, for some reason Tornatore got most of the best ones.
2 - The more dated stuff that was experimental at the time and was influenced by concrete music, with a variable amount of lyricism. They were used in thrillers, horror films and cops/robbers stories, often by European directors.
3 - The Battle of Algier kind of Morricone, that I wouldn't know how to describe.
Depending on the movie, Leone got pieces from the three kinds of Morricone, usually great ones. In OUATITW and DYS, he got a mix of the three, and that's when I find Ennio's work absolutely powerful. The only thing that Leone didn't get is the Morricone from the 80's-90's Hollywood stuff (Frantic, Disclosure...), which is cool because it usually sucks.