I love 1 & 2. They’re modern morality plays, imho.
I believe that had the third movie NOT been a sequel (e.g. just a story about an aging Mafioso facing his own immorality and the politics of his empire), that it would be regarded as a very good Mafia movie. Unfortunately, it was a sequel to two masterpieces and it simply doesn't stand up. The fact that it was released at the same time as "Goodfellas" diminishes it even more.
I think the thing that really made the first two movies was Robert Duvall's portrayal of Tom Hagen. On the surface he was very calm and nonviolent, but in reality he was possibly the coldest and most ruthless of all.