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

Yes

The word "dos" is a contraction of the preposition de (of/from) and the masculine plural definite article os (the). In both Brazilian and Continental Portuguese, the meaning, grammatical function, and spelling of the word are identical. The only difference is pronunciation:

• In Brazilian Portuguese, the "s" is often pronounced as a soft "s" [s] (common in São Paulo) or a "sh" [ʃ] (common in Rio de Janeiro), and the vowels are typically more open.
• In Continental Portuguese, the "s" at the end of the word is almost always pronounced as a "sh" [ʃ] sound, and the vowels are typically more closed or reduced.

Brazilian Portuguese Examples

1. Eu gosto muito dos meus amigos. (I like my friends very much.)
2. Eu estou gostando dos novos jogos. (I am liking the new games.) Note: Use of the gerund "-ndo".
3. O preço dos brinquedos é muito caro. (The price of the toys is very expensive.)
4. Eu vi a foto dos cachorros. (I saw the photo of the dogs.)
5. Os nomes dos meninos estão na lista. (The boys' names are on the list.)

Portuguese (Portugal) Examples

1. Eu gosto muito dos meus amigos. (I like my friends very much.)
2. Eu estou a gostar dos novos jogos. (I am liking the new games.) Note: Use of "a" + infinitive.
3. O preço dos brinquedos é muito elevado. (The price of the toys is very high.)
4. Eu vi a fotografia dos cães. (I saw the photograph of the dogs.)
5. Os nomes dos miúdos estão na lista. (The kids' names are on the list.)