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

Yes

The only difference between the use of "noite" in Brazilian Portuguese and Continental Portuguese is pronunciation. The spelling, meaning, and grammatical function are identical in both dialects.

In Brazilian Portuguese, the vowels are generally more open and clearly articulated; the final "e" is typically pronounced as a clear "ee" sound (/ˈnoj.tʃi/). In Continental Portuguese, unstressed vowels tend to be more reduced or "swallowed." The final "e" is much more closed and subtle, often sounding like a very short, near-silent neutral vowel (/ˈnoj.tɨ/).

Brazilian Portuguese

1. Boa noite, tudo bem com você? (Good evening, is everything well with you?)
2. Eu gosto de caminhar à noite. (I like to walk at night.)
3. A noite está muito bonita hoje. (The night is very beautiful today.)
4. Eu vou sair hoje à noite. (I am going to go out tonight.)
5. Ele trabalha durante a noite. (He works during the night.)

Continental Portuguese

1. Boa noite, tudo bem? (Good evening, is everything well?)
2. Gosto de caminhar à noite. (I like to walk at night.)
3. A noite está muito bonita hoje. (The night is very beautiful today.)
4. Vou sair esta noite. (I am going to go out tonight.)
5. Ele trabalha à noite. (He works at night.)