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

Yes

The word "catedral" is identical in spelling, meaning, and grammatical gender in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more "open" and clearly articulated. In Continental Portuguese, unstressed vowels are often "reduced" or closed, meaning the "e" in the middle of the word might be pronounced much more softly, almost swallowed, making the word sound more consonant-heavy and clipped.

Brazilian Portuguese Examples

1. A Catedral da Sé é um ponto turístico muito famoso em São Paulo. (The Sé Cathedral is a very famous tourist landmark in São Paulo.)
2. Eu adoro a arquitetura daquela catedral antiga. (I love the architecture of that old cathedral.)
3. Vamos nos encontrar na frente da catedral às oito horas? (Shall we meet in front of the cathedral at eight o'clock?)
4. A catedral fica bem no meio da praça principal. (The cathedral is right in the middle of the main square.)
5. Eles construíram uma catedral enorme para a celebração. (They built a huge cathedral for the celebration.)

Continental Portuguese Examples

1. A Catedral de Lisboa é um monumento histórico essencial. (Lisbon Cathedral is an essential historical monument.)
2. Passei pela catedral para ver os vitrais novos. (I passed by the cathedral to see the new stained glass.)
3. A catedral é o grande marco da nossa cidade. (The cathedral is the great landmark of our city.)
4. Estávamos à porta da catedral quando começou a chover. (We were at the cathedral door when it started to rain.)
5. A catedral é o coração deste bairro antigo. (The cathedral is the heart of this old neighborhood.)