A large brain does offer some advantages, but size isn't everything as it depends on how you use it.
It's a common misconception that because we only use a small part of our brain at any one time that if we could use more, or indeed all of it, then we would be so much more intelligent.
Truth is, as shown by scans of people carrying out various tasks, we do use all of our brain, but not all at once. Which makes sense otherwise I'm pretty sure we would run the risk of 'crashing' just like an overloaded computer.
Dolphins have bigger brains than we do but studies seem to suggest that most of it deals with communication with only limited problem solving, on the other hand we excell at problem solving and that, more than just overall brain capacity, is what probably gave us a signifcant advantage over our rivals.
