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

Yes

The word "palavras" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, vowels in unstressed syllables tend to be more open and clearly articulated. In Continental Portuguese, unstressed vowels (such as the "a" in "palavras") are often reduced or "closed," sounding more like a neutral "uh" sound (schwa).

Brazilian Portuguese examples:

1. Eu não entendi essas palavras. (I didn't understand these words.)
2. Ele disse palavras muito bonitas. (He said very beautiful words.)
3. As palavras dele me magoaram. (His words hurt me.)
4. Escreva as palavras no caderno. (Write the words in the notebook.)
5. Existem muitas palavras difíceis aqui. (There are many difficult words here.)

Continental Portuguese examples:

1. Eu não percebi estas palavras. (I didn't understand these words.)
2. Ele disse palavras muito bonitas. (He said very beautiful words.)
3. As palavras dele magoaram-me. (His words hurt me.)
4. Escreve as palavras no caderno. (Write the words in the notebook.)
5. Há muitas palavras difíceis aqui. (There are many difficult words here.)