Metal Gear Solid 2 > Metal Gear Solid.
As much as I enjoyed playing as Snake, the whole idea of him being a sort of outside figure to the mission was a really neat addition in my eyes, and the whole banter between him and Otacon at the first part was just too good.
I always preferred Dead Cell to Foxhound, although I never found Vamp that interesting of a character; he seemed to have been placed in the story solely as a plot device for Fortune, and to get the final part of the story going.
But still, I agree that MGS had a fantastic/if not better story (or at least one that wasn't so hard to wrap your head around), and people liked the characters more, but in terms of gameplay, cutscenes, graphics, and overall content of the game (note this is from the EU version, which had the likes of boss rush, and that crazy cutscene editor included as standard) were much better than the first game.