"Better" depends on your point of view. If you want your daughter to excel in pure academics (math, english, science), then Cupertino schools are excellent. If you want your daughter to explore some of her hobbies (like art, fencing, etc.) then a private school like Harker would be good. There's no right or wrong. Just depends on your vision of what you would like your daughter to be. The kids I know who go to Harker don't care as much about getting a high paying job as much as doing what they enjoy (e.g. art, history, etc.). The kids I know who went to Cupertino schools ended up going to medical school, law school, high tech, etc. Which path do you want your daughter to take? Which path does your DAUGHTER want to take?
Please note: I'm just telling you my experience from my circle of friends, past clients, etc. and their children who went to public vs. private school. You will want to gather a larger sample set.