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

No

While the spelling and fundamental meaning of "branco" are identical, there are differences in typical usage and pronunciation. In Brazil, the word is frequently paired with the verb dar (e.g., deu um branco) to describe a momentary memory lapse, whereas in Portugal, the verb ter (e.g., tive um branco) is much more natural. Additionally, Brazilian pronunciation is more open and clearly articulated, while Continental Portuguese features more reduced and "closed" vowels.

Brazilian Portuguese

1. Eu comprei um carro branco. (I bought a white car.)
2. O papel está todo branco. (The paper is all white.)
3. Deu um branco na minha cabeça. (My mind went blank.)
4. Ela comprou uma blusa branca. (She bought a white blouse.)
5. O espaço em branco é pequeno. (The blank space is small.)

Continental Portuguese

1. Comprei um automóvel branco. (I bought a white car.)
2. A folha está toda branca. (The sheet/paper is all white.)
3. Tive um branco durante o exame. (I had a blank during the exam.)
4. Ela usa uma camisola branca. (She is wearing a white sweater.)
5. O campo em branco deve ser preenchido. (The blank field must be filled.)