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SPOILERS
I thought both sections were pretty good. The story is more engrossing once the aliens come out and play but both sections have a pretty decent story I think. Gameplay is probably better when the Koreans are your main enemy though, though fighting the aliens was still fun, especially in the ship and climbing down the mountain and on the carrier. Story's not as good as Half Life 2's, but still a pretty decent story, even if it has been done before more or less.
The only level I didn't like in Crysis was the VTOL mission. The controls felt pretty bad and I felt like it was a level that was just added in for the hell of it. It was pretty cool how it ended though flying off the island escaping the aliens, but they could have had that scene by making your way on foot to an evac.
The last level was really amazing and well done, graphically and gameplay wise. I found it created a great atmosphere as well. Seeing the hundreds of aliens fly by in the night as others assault the carrier was really impressive. The explosions looked really good on that level and it ran pretty fluidly on a mix of medium, high and very high settings, and shadows on low.
I hope the next Crysis games will have a fair mix of human combat as well. I don't know how they will manage that but hopefully they will. Because the aliens are cool to fight, especially the big boss fights but the other enemies get annoying after a while, especially the ones that are always flying in the sky, though they are cool.
Overall though, a great game. I look forward to the day where we can max it easily like Far Cry today.