Contemporary research is a mixture of both, as scientists compete for the funding they need to carry out their projects, but collaboration on various levels is highly valued and actively encouraged. As someone mentioned in the thread, nobody wants to be sitting on pieces of the puzzle when they can finish it together.
However, I chose Collaborative because I feel that the competitive culture in academia (particularly in the US and Europe, and in natural sciences) causes some big problems. The competition for funding means that researchers come up with more and less brilliant ideas, but the grants aren't always given based on the brilliance or usefulness of the project. The researchers that get funded are the ones that manage to sell their project, which means that quite a few good researchers with great projects get dropped in favor of loudmouths, crafty science "salespeople" and friends of people on the grant committee. And even if they get funded, the project report needs to be "sexy" enough to get published ... (In a high-impact journal, anyway; and who wants to be printed the equivalent of some podunk town rag when you can be in the equivalent of Time and Frankfurter Allgemeine?)