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

No.

While the spelling, grammar, and core dictionary meanings of "enfim" are identical in both dialects, there is a difference in typical usage and connotation. In Brazilian Portuguese, "enfim" is frequently used as a neutral, functional transition to summarize a topic or move a conversation toward a conclusion (similar to "anyway" or "in short"). In Continental Portuguese, while it can be used this way, it carries a much heavier connotation of resignation, exasperation, or finality—often acting as a verbal sigh to signal that a situation is settled, even if the outcome is disappointing (similar to "well, what can you do").

Brazilian Portuguese Examples

1. Enfim, vamos embora. (Anyway, let's go.)
2. Enfim, o filme foi muito legal. (In short, the movie was very cool.)
3. Enfim, a chuva parou! (Finally, the rain stopped!)
4. Enfim, não importa o que ele diga. (Anyway, it doesn't matter what he says.)
5. Enfim, ele é um cara muito legal. (In short, he is a very cool guy.)

Continental Portuguese Examples

1. Enfim, vamos embora. (Anyway, let's go.)
2. Enfim, o filme foi muito fixe. (In short, the movie was very cool.)
3. Enfim, a chuva parou! (Finally, the rain stopped!)
4. Enfim, não interessa o que ele diga. (Anyway, it doesn't matter what he says.)
5. Enfim, ele é um tipo muito porreiro. (In short, he is a very cool guy.)