Literally everything. Storyline is better, action set pieces are incredible. Controls are tighter, shooting and movement are way better, and it's a game that still looks great even, what, 7 years after it came out?
The first game is just the proof of concept. The second is probably the best third person action game I've ever played. Maybe the Tomb Raider reboot beats it, but it's close, and that was basically Uncharted With A Lady anyway.
The Last of Us is of course better than either of them, but it kind of transcends genre for me. My feelings on it are nearly identical to Bored's.