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

Yes

The word "feliz" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• In Brazilian Portuguese, the final "i" is clearly articulated, and the "z" is typically pronounced as a soft [s] sound.
• In Continental Portuguese, the final "i" is often reduced or nearly silent (vowel reduction), and the "z" can take on a [ʃ] (sh) sound, making the word sound much shorter and more closed.

Brazilian Portuguese Examples

1. Eu estou muito feliz com a notícia. (I am very happy with the news.)
2. Ela parece uma pessoa muito feliz. (She seems like a very happy person.)
3. Desejo um feliz aniversário para você! (I wish you a happy birthday!)
4. A gente fica muito feliz quando você vem. (We get very happy when you come.)
5. Ele ficou muito feliz ao ganhar o presente. (He became very happy upon winning the gift.)

Continental Portuguese Examples

1. Estou muito feliz com a notícia. (I am very happy with the news.)
2. Ela parece uma pessoa muito feliz. (She seems like a very happy person.)
3. Desejo-te um feliz aniversário! (I wish you a happy birthday!)
4. Nós ficamos muito felizes quando tu vens. (We get very happy when you come.)
5. Ele ficou muito feliz ao receber o presente. (He became very happy upon receiving the gift.)