The short answer is yes and no. Elaborated, L.A. is the center of the film industry, the Mecca if you will. All the big production companies are there. All the distributers are there. All the actors are there. Everyone is there. If you want to rise to the top of the pyramid as a director or producer you should absolutely go to L.A, likewise if you are an actor and want to be in the movies there is no choice, go and don’t look back.
If you would like to be a technician or pursue another crew craft then L.A. is not necessarily the best place right now. Due to out of state tax incentives the work in L.A. has dried up a bit. Many of the California film folk have hit the trail to Massachusetts, Louisiana, or other states offering great incentives. Michigan is now leading the pack with a whopping 42% tax incentive.
The other side of the coin is to consider the quality of life in L.A. The city is a nightmare to get around in; you haven’t seen traffic until you have moved to Los Angeles. You need to consider the lifestyle: I’m not making a judgment; let’s just say it’s not for everyone. If you like L.A. then it is a no brainer. If you don’t go to L.A. you’ll have a harder time winning the academy award. However, if you just want to work somewhere in the industry, there are people all over the U.S making a good living on movies and other media. Figure out your priority, apply my advice and you will know what to do.