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

Yes

The spelling, meaning, and grammatical rules for "contente" are identical in both Brazilian and European Portuguese. The only difference lies in pronunciation. In most Brazilian dialects, the unstressed final "e" is pronounced as a bright, near-close [i] (similar to the "ee" in "see"). In European Portuguese, the final "e" is much more closed and reduced, often sounding like a very short, whispered [ɨ] or becoming almost silent.

Brazilian Portuguese Examples

1. Eu estou muito contente com o resultado. (I am very happy with the result.)
2. Ela ficou super contente com o presente. (She was super happy with the gift.)
3. A gente ficou contente que você veio. (We were happy that you came.)
4. Você não parece muito contente hoje. (You don't seem very happy today.)
5. Estou contente com o meu novo emprego. (I am happy with my new job.)

European Portuguese Examples

1. Estou muito contente com o resultado. (I am very happy with the result.)
2. Ela ficou muito contente com o presente. (She was very happy with the gift.)
3. Nós ficámos contentes que vieste. (We were happy that you came.)
4. Tu não pareces muito contente hoje. (You don't seem very happy today.)
5. Estás contente com o teu novo emprego? (Are you happy with your new job?)