I lived in New York when I was a kid, but live in the LA area now. It is very different in a lot of ways, but overall, it's not difficult to adapt. Here are some of the major differences.
1. You will need a car. Everything is spread out all over in LA, so you must have a car to get around. The public transportation system is improving, but it doesn't have anywhere near the coverage and convenience of New York (which is a much more densely packed city). At least there's almost always plenty of parking. Be prepared to spend much of your life on the freeways.
2. The weather is great most of the time. Except for a couple of months early in the year when it rains a lot (like right now), you can always plan events to be held outdoors. Even in the hot summer months, it's not humid and miserable, and it always cools down by evening. It snows once every 50 to 100 years, although you can drive an hour or so to the mountains if you really want to see snow in winter.
3. Lots of outdoor activities. I guess this is partly related to weather, but the geography of the LA area also fits into this. There are many beaches and mountains within an hour drive from most parts of LA, so all kinds of outdoor activity is available year-round.
4. The occasional earthquake. It's the price we pay for good weather, I guess. Every few years, we have one, but it's not like they happen all the time. You actually get used to the idea of it. Hurricanes and tornadoes scare me more.
5. Density/Human contact. The fact that LA is spread out is both a plus and a minus, in my opinion. On one hand, I think that generally, LA is a less intimidating place to get around in that it feels a little less urban. However, since most Angelenos just get around in their cars and only walk around when they're at the mall, there's less human contact outside of your own personal sphere. I think that's to our disadvantage.
Otherwise, LA and NY have all the similar advantages and disadvantages of a major metropolis. Cost of living (housing, in particular) is high, there are high crime areas you want to avoid, but there is plenty of arts, entertainment, nightlife and culture to keep you occupied. And maybe you'll get to be in a movie! For someone coming to LA from New York, if you can adapt to the car culture, everything else should be fairly straightforward. As the famous song about New York says, if you can make it there, you'll make it anywhere!