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

Yes

The word "coisa" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. It functions as a universal placeholder for objects, situations, or ideas that are unknown, unnamed, or too vague to describe. The only significant difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, there is a higher degree of vowel reduction; the "o" may sound more like a closed "u" or a very short, neutral sound, and the final "a" is often swallowed or much more subtle.

Brazilian Portuguese Examples

1. Eu não entendi essa coisa. (I didn't understand this thing.)
2. Tem uma coisa para te falar. (There is something to tell you.)
3. Essa coisa está quebrada. (This thing is broken.)
4. Não faz essa coisa de novo. (Don't do that thing again.)
5. Essa coisa é muito legal! (This thing is very cool!)

Continental Portuguese Examples

1. Eu não percebi essa coisa. (I didn't understand this thing.)
2. Tenho uma coisa para te dizer. (I have something to tell you.)
3. Esta coisa está partida. (This thing is broken.)
4. Não faças essa coisa outra vez. (Don't do that thing again.)
5. Esta coisa é muito fixe! (This thing is very cool!)