At the start let me warn you that I am biased toward NYU. My daughter is currently attending NYU Tisch for Film and has had Summer Internships in LA the past two summers, while also interning in NY during the year. So just because you’re in NY doesn’t exclude internships in LA. When choosing a college we visited lots of west coast schools like USC, Chapman and UCLA, but unfortunately LMU wasn’t one of them so I can’t compare campuses. What I can say is that my daughter has met people from all over the world at NYU. It truly is a very diverse campus and she even spent one semester abroad at FAMU in the Czech Republic and shot a film while there that was a finalist in a film festival. NYU really encourages their students to study abroad at least one semester. The films produced are as varied as the student population and living at NYU is truly living in New York City which is home to a vibrant entertainment community. You can even combine your film degree with a minor that includes the business side of the entertainment world and take courses at NYU’s Stern school of business.
Here is one article that talks about the films being made in NYC.
http://www.latimes.com/entertainment/envelope/cotown/la-et-ct-ny-la-rivalry-20140503-story.html
About competition - Film is a cooperative venture, no one can make a film themselves and during her time at NYU, my daughter has spent time doing every job that you can do on set from starting out as a PA to being the Writer and Director on her own. I’ve never heard her say anything negative about her fellow film students.
Someone else mentioned above, cost is a big factor. However, I think LMU is in the same range as NYU, so unless there is some financial aid being offered, I don’t think there is a big difference in cost.
In the end, it’s up to you. Your own feeling about which place will be best for YOU, but despite what you choose, if you’re passionate about what you do, I’m sure you’ll be a success. Good luck!