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

No

While the spelling and core meaning of "personagem" are identical in both Brazilian and European Portuguese, there are differences in typical usage and the surrounding syntax. In Brazil, it is common and widely accepted to use the word in both the masculine (o personagem) and feminine (a personagem) forms. In Portugal, however, the feminine form is much more standard and preferred. Additionally, the syntactic structures used in conjunction with the word differ; Brazilians frequently use the gerund (interpretando), whereas Portuguese people typically use the preposition "a" followed by the infinitive (a interpretar).

Brazilian Portuguese Examples

1. "A personagem principal do livro é muito corajosa." (The main character of the book is very brave.)
2. "Ele interpreta um personagem muito engraçado na novela." (He plays a very funny character in the soap opera.)
3. "Eu não consegui me identificar com essa personagem." (I couldn't identify with this character.)
4. "O autor criou personagens muito bem desenvolvidos." (The author created very well-developed characters.)
5. "Aquele ator é ótimo interpretando personagens vilões." (That actor is great at playing villain characters.)

Portuguese (Portugal) Examples

1. "A personagem principal do livro é muito corajosa." (The main character of the book is very brave.)
2. "Ele interpreta uma personagem muito engraçada na telenovela." (He plays a very funny character in the soap opera.)
3. "Não me consegui identificar com esta personagem." (I couldn't identify with this character.)
4. "O autor criou personagens muito bem desenvolvidos." (The author created very well-developed characters.)
5. "Aquele ator é excelente a interpretar personagens vilões." (That actor is excellent at playing villain characters.)