I guess in a way, I want to show those people that I can be as good, or better, as them.
It should be "I want to show those people that I can be as good as, or better than them."
What people are you talking about though? That could help make the sentence better if you are more descriptive, unless of course you described "thosepeople" in the previous sentences.
As for UCSD it's not easy to get into, but it's a party school for sure. I had a friend who went there but transferred for that very reason.
