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

Yes

The word "parte" is identical in meaning, grammar, and spelling in both Brazilian and European Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the unstressed final "e" is typically pronounced as a clear, light /i/ sound (sounding like "par-chee"). In European Portuguese, the final "e" is much more reduced, often sounding like a very short, nearly silent /ɨ/ or almost disappearing entirely in rapid speech.

Brazilian Portuguese Examples

1. Eu faço parte da equipe. (I am part of the team.)
2. Essa é a parte mais difícil. (That is the most difficult part.)
3. Uma parte do bolo sumiu. (A part of the cake disappeared.)
4. Ele não fez a parte dele. (He didn't do his part.)
5. Essa parte do livro é legal. (That part of the book is cool.)

European Portuguese Examples

1. Eu faço parte da equipa. (I am part of the team.)
2. Esta é a parte mais difícil. (This is the most difficult part.)
3. Uma parte do bolo desapareceu. (A part of the cake disappeared.)
4. Ele não fez a sua parte. (He didn't do his part.)
5. Esta parte do livro é gira. (This part of the book is nice.)