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

Yes.

The word "nossos" is identical in spelling, meaning, and grammatical function (possessive adjective/pronoun) in both Brazilian and Continental Portuguese. The only difference lies in pronunciation (phonology). In Brazilian Portuguese, vowels tend to be more open and clearly articulated, and the "s" at the end of syllables is generally pronounced as a soft "s" (as in "sun"). In Continental Portuguese, vowels are often more closed or "reduced" (making the word sound shorter/more swallowed), and the "s" at the end of syllables is frequently pronounced as "sh" (as in "shoe").

Brazilian Portuguese Examples

1. Nossos amigos chegaram cedo. (Our friends arrived early.)
2. Onde estão os nossos celulares? (Where are our cell phones?)
3. Nossos ônibus estão atrasados. (Our buses are late.)
4. Adoro os nossos planos para as férias. (I love our plans for the holidays.)
5. Nossos cachorros adoram brincar. (Our dogs love to play.)

European Portuguese Examples

1. Nossos amigos chegaram cedo. (Our friends arrived early.)
2. Onde estão os nossos telemóveis? (Where are our cell phones?)
3. Os nossos autocarros estão atrasados. (Our buses are late.)
4. Adoro os nossos planos para as férias. (I love our plans for the holidays.)
5. Os nossos cães adoram brincar. (Our dogs love to play.)