T-Ball is instructional, Farm is supposed to be instructional but is actually quite competitive. Minors is even more competitive.
Kids are naturally competitive when it comes to sports.
I think what it comes down to is the coaches and how they approach the game. They need to set the example, I always try to make the game fun for the entire team. We practice hard, play the games hard and fair, learn from our mistakes and at all times have lots of fun. I try to emphasize that while we are competing against another team, we are trying to best our play from the prior game as a team and indivdually. Some coaches are way to competitive for the age group they are coaching.