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

Yes

The word "branca" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the unstressed final "a" is generally pronounced with a more open vowel sound. In Continental Portuguese, unstressed vowels are often reduced or "swallowed," making the final "a" sound much more closed and subtle.

Brazilian Portuguese Examples

1. A casa dela é toda branca. (Her house is all white.)
2. Eu comprei uma blusa branca ontem. (I bought a white blouse yesterday.)
3. A nuvem branca sumiu no céu. (The white cloud disappeared in the sky.)
4. Ela tem a pele muito branca. (She has very white skin.)
5. A flor branca é muito cheirosa. (The white flower is very fragrant.)

Continental Portuguese Examples

1. A casa dela é toda branca. (Her house is all white.)
2. Eu comprei uma blusa branca ontem. (I bought a white blouse yesterday.)
3. A nuvem branca desapareceu no céu. (The white cloud disappeared in the sky.)
4. Ela tem a pele muito branca. (She has very white skin.)
5. A flor branca é muito cheirosa. (The white flower is very fragrant.)