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

Yes

The meaning, spelling, and grammar of the word "assunto" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazil, vowels are generally more open, and the "s" is typically pronounced as a clear "ss" sound. In Portugal, vowels are often "reduced" (becoming shorter or more closed), and the "s" frequently takes on a "sh" sound (known as chiado) when it appears before consonants or at the end of syllables, depending on the region.

Brazilian Portuguese Example Sentences

1. Eu estou mudando de assunto. (I am changing the subject.)
2. Ele está falando sobre um assunto muito sério. (He is talking about a very serious subject.)
3. Não temos nenhum assunto para conversar hoje. (We don't have any topic to talk about today.)
4. Esse assunto está ficando muito complicado. (This subject is getting very complicated.)
5. Nós vamos tratar desse assunto amanhã. (We are going to deal with this matter tomorrow.)

Continental Portuguese Example Sentences

1. Eu estou a mudar de assunto. (I am changing the subject.)
2. Ele está a falar sobre um assunto muito sério. (He is talking about a very serious subject.)
3. Não temos nenhum assunto para conversar hoje. (We don't have any topic to talk about today.)
4. Este assunto está a tornar-se muito complicado. (This subject is becoming very complicated.)
5. Nós vamos tratar desse assunto amanhã. (We are going to deal with this matter tomorrow.)