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

Yes

The only difference between "artes" in Brazilian Portuguese and Continental Portuguese is pronunciation. In Brazilian Portuguese, the unstressed "e" is articulated clearly, usually sounding like a closed /e/ or a soft /i/. In Continental Portuguese, unstressed vowels are heavily reduced; the "e" is often swallowed or pronounced as a very short, almost silent, central vowel (/ɨ/), making the word sound much closer to "art's" in English.

Brazilian Portuguese Examples

1. Eu estou estudando artes visuais. (I am studying visual arts.)
2. Ele faz artes marciais todas as manhãs. (He does martial arts every morning.)
3. Nós estamos aprendendo as artes do desenho. (We are learning the arts of drawing.)
4. Ela está fazendo artes manuais no fim de semana. (She is doing crafts on the weekend.)
5. Você gosta de apreciar as artes? (Do you like to appreciate the arts?)

Continental Portuguese Examples

1. Eu estou a estudar artes visuais. (I am studying visual arts.)
2. Ele pratica artes marciais todas as manhãs. (He practices martial arts every morning.)
3. Nós estamos a aprender as artes do desenho. (We are learning the arts of drawing.)
4. Ela está a fazer artes manuais no fim de semana. (She is doing crafts on the weekend.)
5. Tu gostas de apreciar as artes? (Do you like to appreciate the arts?)