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

Yes

The only differences between "engenheiro" in Brazilian Portuguese and Continental Portuguese are phonetic. In Brazil, the unstressed vowels are generally more open and clearly articulated. In Portugal, unstressed vowels (such as the "e" in the middle of the word) undergo significant reduction, often sounding much more closed or nearly silent, which gives the word a more clipped sound.

Brazilian Portuguese Examples

1. Ele é um engenheiro civil muito competente. (He is a very competent civil engineer.)
2. Eu quero ser engenheiro de computação. (I want to be a computer engineer.)
3. O engenheiro está conferindo a planta da obra. (The engineer is checking the construction blueprint.)
4. Precisamos contratar um engenheiro de produção. (We need to hire a production engineer.)
5. O prédio foi projetado por um engenheiro renomado. (The building was designed by a renowned engineer.)

Continental Portuguese Examples

1. Ele é um engenheiro civil muito competente. (He is a very competent civil engineer.)
2. Eu quero ser engenheiro informático. (I want to be a computer engineer.)
3. O engenheiro está a verificar o projeto da obra. (The engineer is checking the construction project.)
4. Precisamos de contratar um engenheiro de produção. (We need to hire a production engineer.)
5. O edifício foi projetado por um engenheiro renomado. (The building was designed by a renowned engineer.)