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

Yes.

The spelling, meaning, and grammar of the word "aniversários" are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazil, the vowels are generally more open, and the "s" at the end of the word is pronounced as a soft [s]. In Portugal, the vowels are more closed (often reduced or almost silent), and the final "s" is pronounced as [ʃ], similar to the "sh" in the English word "shoe."

Brazilian Portuguese Examples

1. Eu amo celebrar aniversários com meus amigos. (I love celebrating birthdays with my friends.)
2. Meus aniversários de infância foram muito felizes. (My childhood birthdays were very happy.)
3. Nós temos muitos aniversários para festejar este mês. (We have many birthdays to celebrate this month.)
4. Ela sempre organiza festas de aniversários incríveis. (She always organizes incredible birthday parties.)
5. Você lembra dos aniversários da nossa família? (Do you remember our family's birthdays?)

European Portuguese Examples

1. Adoro celebrar os meus aniversários com os meus amigos. (I love celebrating my birthdays with my friends.)
2. Os meus aniversários de infância foram muito felizes. (My childhood birthdays were very happy.)
3. Temos imensos aniversários para festejar este mês. (We have many birthdays to celebrate this month.)
4. Ela organiza sempre festas de aniversários incríveis. (She always organizes incredible birthday parties.)
5. Lembras-te dos aniversários da nossa família? (Do you remember our family's birthdays?)