Is the word passagem the same in Brazilian and European Portuguese?

No.

The difference lies in typical usage. In Brazil, "passagem" is the standard word used to refer to a travel ticket (for buses, planes, etc.). In Portugal, while "passagem" is understood, the word "bilhete" is much more common for transport. Additionally, when expressing the same idea, a Portuguese person would use different vocabulary for the vehicles themselves (for example, autocarro instead of ônibus and comboio instead of trem).

Brazilian Portuguese Examples

1. Eu comprei minha passagem de avião ontem. (I bought my plane ticket yesterday.)
2. A passagem de ônibus está muito cara. (The bus ticket is very expensive.)
3. Li uma passagem linda nesse livro. (I read a beautiful passage in this book.)
4. A passagem do tempo é inevitável. (The passage of time is inevitable.)
5. Ele perdeu a passagem de trem. (He lost his train ticket.)

Continental Portuguese Examples

1. Eu comprei o meu bilhete de avião ontem. (I bought my plane ticket yesterday.)
2. O bilhete de autocarro está muito caro. (The bus ticket is very expensive.)
3. Li uma passagem linda neste livro. (I read a beautiful passage in this book.)
4. A passagem do tempo é inevitável. (The passage of time is inevitable.)
5. Ele perdeu o bilhete de comboio. (He lost his train ticket.)