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Teach your kids your values, and to be the best they can be. But whatever you do, when you have kids, do NOT make them compete against each other for your affections. Your love, support, and attention should be given to all equally, regardless of who is the "best."

In certain areas of life, as Monster said, say sports, skill competitions, etc., winning and striving to win are reasonable goals. But in every day life, people who focus on outdoing other people just because they can tend to be arrogant assholes, or at the very least neurotic and unpleasant. No one wants to be around them. They are the kind of people who would sabotage their coworkers, belittle their friends, and fight over their parents' estates to get the bigger share. Those are my opinions, and may be beyond the scope of what you are really talking about though, fresh.