Taking the second CD first, since the music here is older, the big track Here is the fat man, originally released as a B-side. The original A-side, Detroit City Blues, is not even included, but I have not heard it so I can not say Whether it was a good decision or not. This CD contains a selection of his early hits on the American R + B charts but not all of them.
The first CD is The One That Appeals of the most, understandably like that. Again, the really big hits are here, but there's plenty missing if you are comparing the tracks listed with the chars.
This is a nice introduction to Fats Domino's music of the fifties, but by No Means definitive. If you enjoy this, you'll likely end up looking to add another compilation fact contains some of the music omitted from this set, Including some of his sixties music.