Even though none will exist without each other, I think I should vote for science. Arts in the other hand, isn't something that is 'needed' in the sense of human survival. In fact, there were ages of human civilisation, without any form of arts or literature. The mankind survived just fine. The scientific development is essential, as it is the only thing that drive mankind forward
Science is more beneficial to your lifetime then drama, arts and other activities like that. Sure these activities allow you to have a more social life, but science will be more helpful in your life as we develop more technologies that could increase your standard of living. What I am trying to say is that without science we would be completely oblivious to the events that happen around us. People can live without drama, music, and visual art.
Honestly, this could go in either category, but it really just depends on the situation. If it was a medical issue, then science would be the way to go. If it was depression, sadness, or some other thing, the arts would be better. Science is how stuff works. To me, a song sounds a lot better and more satisfying than someone explaining to me scientifically why I am happy. But, if I was in the ER with a broken bone, science would be a lot better telling me how they can fix it rather than listening to a song.
Studies have shown that there are parts of the brain that can only be developed through exercising the arts, such as music and dance. If we allow these things to fall out of our lives, there is a great deal of mental potential that is being wasted, let alone the absence of relationships and entertainment with these gone. Also, I don't think it is possible to entirely separate Science and Art. You can't understand how to create music or paint a picture without knowing how these activities are structured, and any science is beautiful when you look at it the right way.