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

Yes

The difference between "trabalha" in Brazilian and Continental Portuguese is purely phonetic. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels undergo significant reduction; therefore, the unstressed "a" sounds in "trabalha" are often "swallowed" or pronounced much more closed, making the word sound more clipped or abbreviated to a Brazilian ear.

Brazilian Portuguese

1. Ele trabalha muito. (He works a lot.)
2. Ela trabalha na padaria. (She works at the bakery.)
3. O seu irmão trabalha aqui? (Does your brother work here?)
4. Você trabalha no sábado? (Do you work on Saturday?)
5. Ela trabalha em uma loja. (She works in a shop.)

Continental Portuguese

1. Ele trabalha imenso. (He works a lot.)
2. Ela trabalha numa padaria. (She works in a bakery.)
3. O teu irmão trabalha aqui? (Does your brother work here?)
4. O senhor trabalha ao sábado? (Do you work on Saturday?)
5. Ela trabalha numa loja. (She works in a shop.)