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

No

While the word "passatempo" is used in both dialects to refer to a hobby or a pastime, there is a significant difference in its meaning and typical usage.

In Brazil, "passatempo" refers almost exclusively to a hobby, an activity done for leisure, or a puzzle (like a crossword). If a Brazilian wants to refer to a giveaway, a sweepstakes, or a competition hosted by a brand or media outlet, they would naturally use words like concurso or sorteio.

In Portugal, "passatempo" retains the meaning of "hobby," but it is also the standard, primary word used to describe a "contest," "giveaway," or "sweepstakes" (e.g., a radio station contest).

Brazilian Portuguese Examples

1. Ler é o meu passatempo favorito. (Reading is my favorite pastime.)
2. O que você gosta de fazer como passatempo? (What do you like to do as a hobby?)
3. Ele não tem nenhum passatempo além de jogar futebol. (He doesn't have any hobby other than playing soccer.)
4. Desenhar é um passatempo muito relaxante. (Drawing is a very relaxing pastime.)
5. Eu adoro este livro de passatempos. (I love this book of puzzles.)

Continental Portuguese Examples

1. Ler é o meu passatempo favorito. (Reading is my favorite pastime.)
2. O que fazes como passatempo? (What do you do as a hobby?)
3. Ele não tem nenhum passatempo além de jogar futebol. (He doesn't have any hobby other than playing soccer.)
4. Desenhar é um passatempo muito relaxante. (Drawing is a very relaxing pastime.)
5. Eu ganhei um prémio num passatempo da rádio. (I won a prize in a radio contest.)