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

Yes

The word "trabalho" is semantically, grammatically, and orthographically identical in both Brazilian and Continental Portuguese. The primary difference lies in pronunciation.

In Brazilian Portuguese, the vowels are generally more "open" and clearly articulated. The first "a" is pronounced as a bright /a/. In Continental Portuguese, vowels are often "reduced" or "closed"; the first "a" is swallowed and sounds more like a neutralized /ɐ/ (similar to the 'a' in "about"). Additionally, the consonants in European Portuguese are often more "clipped," whereas Brazilian Portuguese tends to be more melodic and syllabic.

Brazilian Portuguese Examples

1. Eu tenho muito trabalho hoje. (I have a lot of work today.)
2. Onde fica o seu trabalho? (Where is your workplace/job?)
3. Eu terminei meu trabalho de escola. (I finished my school assignment.)
4. O trabalho dele é muito legal. (His job is very cool.)
5. Você já começou o seu trabalho? (Have you already started your work?)

Continental Portuguese Examples

1. Tenho muito trabalho hoje. (I have a lot of work today.)
2. Onde é o teu trabalho? (Where is your work?)
3. Acabei o meu trabalho de casa. (I finished my homework.)
4. O trabalho dele é muito porreiro. (His job is very cool.)
5. Já começaste o teu trabalho? (Have you already started your work?)