Why do other team members have higher level crowns, but I score more that the other team members?

You earn crown point credits in the tournaments. Tournaments are usually weekends. By participating in the tournament, you can boost your crown points by 20-50 points. The higher Crown points are awarded when placing in the top 3 tournament players in your 100-player’s tournament group.

The other team members are likely joining into the tournament later in the weekend, or picking a time when less-competitive players are joining. They don't need to get as many words to do better in the tournament. Thus, they get more crown points/medals, but they don't get as many words (lower brilliance).