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

Yes

The word "campo" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the nasalized vowel "am" is typically more open and resonant, and the rhythm of the word follows the more melodic, syllable-timed nature of Brazilian speech. In Continental Portuguese, the "a" in the nasal diphthong is more closed and the pronunciation is more clipped and subtle.

Brazilian Portuguese

1. Eu adoro passar o fim de semana no campo. (I love to spend the weekend in the countryside.)
2. O jogador chutou a bola para fora do campo. (The player kicked the ball out of the field.)
3. Ela está fazendo uma pesquisa de campo. (She is doing field research.)
4. O campo de futebol está muito molhado. (The soccer field is very wet.)
5. Este é o meu campo de atuação. (This is my field of expertise/action.)

Continental Portuguese

1. Eu adoro passar o fim de semana no campo. (I love to spend the weekend in the countryside.)
2. O jogador rematou a bola para fora do campo. (The player struck the ball out of the field.)
3. Ela está a fazer uma investigação de campo. (She is doing field research.)
4. O campo de futebol está muito molhado. (The soccer field is very wet.)
5. Este é o meu campo de atuação. (This is my field of expertise/action.)