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

Yes.

The word "escuro" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The differences are strictly phonetic:

• The "s" sound: In Brazilian Portuguese, the "s" is typically pronounced as a sibilant /s/ (as in "sun"). In Continental Portuguese, the "s" before a consonant is pronounced as a postalveolar fricative /ʃ/ (as in "she").
• Vowel quality: The initial "e" is generally more open in Brazil, whereas in Portugal, it can be more closed or even reduced in certain phonetic environments.

Brazilian Portuguese

1. O quarto está muito escuro. (The room is very dark.)
2. Eu gosto de azul escuro. (I like dark blue.)
3. Está ficando escuro lá fora. (It is getting dark outside.)
4. Ela tem olhos escuros. (She has dark eyes.)
5. Não gosto de andar em lugares escuros. (I don't like walking in dark places.)

Continental Portuguese

1. O quarto está muito escuro. (The room is very dark.)
2. Eu gosto de azul escuro. (I like dark blue.)
3. Está a ficar escuro lá fora. (It is getting dark outside.)
4. Ela tem olhos escuros. (She has dark eyes.)
5. Não gosto de andar em sítios escuros. (I don't like walking in dark places.)