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

No.

While the dictionary definitions are very similar, there is a difference in typical usage. In Brazilian Portuguese, "faculdade" is the standard, everyday term used to refer to the institution of higher education as a whole (similar to "college" or "university" in English). In Continental Portuguese, "universidade" is the standard term for the institution, whereas "faculdade" is more specifically used to refer to a particular department or division within that university (e.g., the Faculty of Law).

Brazilian Portuguese Examples

1. Eu terminei a faculdade ano passado. (I finished college last year.)
2. A faculdade dele é muito longe de casa. (His college is very far from home.)
3. Você já escolheu qual faculdade vai fazer? (Have you already chosen which college you're going to attend?)
4. Eu preciso comprar livros para a faculdade. (I need to buy books for college.)
5. A faculdade de Medicina é muito concorrida. (The medical school is very competitive.)

Continental Portuguese Examples

1. Eu terminei a licenciatura no ano passado. (I finished my degree last year.)
2. A universidade dele é muito longe de casa. (His university is very far from home.)
3. Já decidiste que curso vais fazer na universidade? (Have you decided which course you're going to do at the university?)
4. Preciso de comprar livros para a universidade. (I need to buy books for the university.)
5. A faculdade de Medicina é muito concorrida. (The Faculty of Medicine is very competitive.)