I've generally had the opposite experience. Carcassone is simpler, and a player can generally play competently on their first game.
Catan, on the other hand, I've found difficult to teach, despite the rules being fairly obvious to me, and there's lots of edge-case rules. (I had one friend get fairly pissed at me that I didn't describe, at the beginning of the game, the rule that a new settlement can break a longest road, which is a rule that hardly ever comes up)
Edit:
That said, Catan probably is a better gateway game into European-style board games in general, since it uses many of the same concepts.
Ticket to Ride would probably be my top pick now, though, for a gateway game.
Catan, on the other hand, I've found difficult to teach, despite the rules being fairly obvious to me, and there's lots of edge-case rules. (I had one friend get fairly pissed at me that I didn't describe, at the beginning of the game, the rule that a new settlement can break a longest road, which is a rule that hardly ever comes up)
Edit: That said, Catan probably is a better gateway game into European-style board games in general, since it uses many of the same concepts.
Ticket to Ride would probably be my top pick now, though, for a gateway game.