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

Yes

The word "sobre" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and the "e" is clearly articulated. In Continental Portuguese, the vowels are much more "closed" or reduced; the "e" is often swallowed or pronounced as a very faint, almost silent schwa-like sound.

Brazilian Portuguese

1. Eu li um livro sobre a história do Brasil. (I read a book about the history of Brazil.)
2. O celular está sobre a mesa. (The cell phone is on the table.)
3. Nós precisamos falar sobre o problema. (We need to talk about the problem.)
4. O avião voou sobre as nuvens. (The plane flew over the clouds.)
5. Ele escreveu um artigo sobre ciência. (He wrote an article about science.)

Continental Portuguese

1. Li um livro sobre a história do Brasil. (I read a book about the history of Brazil.)
2. O telemóvel está em cima da mesa. (The mobile phone is on the table.)
3. Nós precisamos de falar sobre o problema. (We need to talk about the problem.)
4. O avião voou por cima das nuvens. (The plane flew over the clouds.)
5. Ele escreveu um artigo sobre ciência. (He wrote an article about science.)