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

Yes

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

In Brazilian Portuguese, the vowels are generally more "open" and clearly articulated. When pronouncing "doentes," a Brazilian speaker will likely pronounce the unstressed "e" in the second syllable clearly. In Continental Portuguese, unstressed vowels tend to be "reduced" or even "swallowed." A Portuguese speaker might pronounce the word with a much more closed or even silent "e," making the word sound more clipped and consonant-heavy.

Brazilian Portuguese Examples

1. As crianças ficaram doentes ontem. (The children got sick yesterday.)
2. Os doentes estão esperando o médico. (The sick [people] are waiting for the doctor.)
3. Eu não gosto de ver pessoas doentes. (I don't like seeing sick people.)
4. Muitos alunos ficaram doentes com a gripe. (Many students got sick with the flu.)
5. Eles parecem muito doentes hoje. (They look very sick today.)

Continental Portuguese Examples

1. As crianças ficaram doentes ontem. (The children got sick yesterday.)
2. Os doentes estão à espera do médico. (The sick [people] are waiting for the doctor.)
3. Não gosto de ver pessoas doentes. (I don't like seeing sick people.)
4. Muitos alunos adoeceram com a gripe. (Many students fell ill with the flu.)
5. Eles aparentam estar doentes hoje. (They appear to be sick today.)