Why is 60FPS sometimes nauseating for me?

So, for the longest time, I've only had low end desktops. They had intel graphics chipsets and could only play really old stuff, and even after I got my first graphics card (Geforce 9800GT.) performance still never reached a solid 60FPS in many things. Thus, I am used to 30 FPS, and it has been very difficult for me to tell the difference except for specific situations. Since then, I've gotten used to watching movies on a 120hz TV, and that was easy to adjust to, and I've seen a video of Sonic Generations at 60FPS, and that is beautiful. However, there are a couple situations in games I felt very odd watching in 60FPS.

Today, I have a low-mid range laptop with an A8-3520M apu. For fun one day, I decided to turn Crysis 1 to low. I also recently started replaying the PC version of Metal Gear Solid 2. In both games, when the cutscenes were being run in 60FPS, motion was smoother than I've ever seen in real life, and it sounded as if the characters were /this/ close to talking over each other - there were practically no pauses between lines of dialogue, and it felt... weird. Gameplay is great in 60FPS, but the differences in the cutscenes were jarring, especially in MGS2's case, where some cutscenes were locked to 30FPS, and others weren't.

Can anyone explain what sort of things I'm experiencing and why?

@Zuon: There are some games where the cutscenes are locked at 30 FPS while the gameplay remains at 60 FPS. It happened in Metal Gear Rising as well, so you're not going crazy. I don't know why devs do that, apart from--maybe--thinking that since the cutscenes are cinematic, 30 FPS makes them feel more so. All it does is disorientate me, to be honest. Stick to one set framerate for the entire game, and you'll be fine when making a game.