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

Yes

The word "hoje" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the final "e" is usually pronounced clearly as [e] or slightly reduced to [i]. In Continental Portuguese, unstressed vowels are much more subject to reduction, so the final "e" is often pronounced as a very short, nearly silent schwa-like sound [ɐ].

Brazilian Portuguese Examples

1. Hoje eu vou ao shopping. (Today I am going to the mall.)
2. O que você vai fazer hoje? (What are you going to do today?)
3. Hoje o dia está muito bonito. (Today the day is very beautiful.)
4. Eu não trabalho hoje. (I am not working today.)
5. Hoje à noite tem uma festa. (Tonight there is a party.)

Continental Portuguese Examples

1. Hoje vou ao centro comercial. (Today I am going to the shopping center.)
2. O que vais fazer hoje? (What are you going to do today?)
3. Hoje o dia está muito bonito. (Today the day is very beautiful.)
4. Não trabalho hoje. (I am not working today.)
5. Hoje à noite há uma festa. (Tonight there is a party.)