Well, just a view points, most in honor of Gould (whose ideas on evolutionary theory I am very fond of).
First, we have been succesful, but the idea of us being "in the lead" or more advanced is not entirely accurate. Evolution works by an animal adapting to take over a niche in the ecosystem. New species typically arise when one of the following occurs:
1. A species dies out or goes extinct, opening a previously filled niche.
2. Climate or environment change, creating new niches to be filled.
3. New lands or areas open up, allowing species to move to niches in new areas.
Now, what's the point of my reiteration of basic biology? I promise, I am getting there
Okay, so, as has been mentioned, humans have two things that set them apart. First we have hands that are capable of fine manipulation of the environment. I specificy fine manipulation because, obviously, even dolphins can manipulate things to a degree, as can other animals. It's the dexterity and versatility of our hands (with opposable thumbs) that's important. Second, we have the ability of language, and again it's a matter of degree. We are able to communicate ideas that are complex, both physcial and abstract concepts.
Now, how does the second paragraph apply to the first?
Well, the ability to manipulate objects allows us to create what we need to fill almost any niche. The ability to communicate means that once one member figures out how to survive, that knowledge can be passed on to others. This helps prevent loss of any survival advantages...social evolution over physical. A new mutation might die out without reproducing...it is much easier to spread knowledge. This means that once we do fill a niche, we tend to be more successful in populating it quickly.
Second, because of our successes and ability to adapt to any niche, we can cause more species to become extinct, opening more niches for us, we can alter our climate on a large scale, causing new niches to open, and we are natural explorers, finding new lands and areas we can fill.
It is precisely because we are not specialized that we are so successful. As to "just beating out" another species, I don't think that's really an issue. They went along a different path; chimpanzees have brains smaller than ours and lack some physical brain structures thought to be critical in communication and higher thought. Elephants lack these structures as well, and also lack manipulative ability. Not to mention that elephants have a more restricted diet. Dolphins, besides the lack of hands, also are limited by their environment (they are made to live in water).
Now my point. Evolution is not really a race. It's more like people filling a theater or concert hall. As long as there are seats open, people try to get in to fill them. We just happen to be good at pointing out empty seats to others of our group, and at elbowing people out of their seats. Not to mention we build a few new ones if there aren't any available
