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

Yes.

The only difference between "dor" in Brazilian Portuguese and Continental Portuguese is pronunciation. In Brazil, the "o" is typically more open, and the final "r" is often pronounced more distinctly (sometimes as a retroflex "r" depending on the region). In Portugal, the "o" is more closed and neutral, and the final "r" is often much softer, more subtle, or nearly silent.

Brazilian Portuguese Examples:

1. Estou com uma dor de cabeça enorme. (I have a huge headache.)
2. Essa dor no pé está me incomodando. (This pain in my foot is bothering me.)
3. Ele sente muita dor na coluna. (He feels a lot of pain in his spine.)
4. A dor de garganta está bem forte. (The sore throat is quite strong.)
5. Não aguento mais essa dor! (I can't stand this pain anymore!)

Continental Portuguese Examples:

1. Sinto uma dor aguda no ombro. (I feel a sharp pain in my shoulder.)
2. Tenho uma dor constante na lombar. (I have a constant pain in my lower back.)
3. A dor é muito incómoda. (The pain is very uncomfortable.)
4. A dor diminuiu após a medicação. (The pain decreased after the medication.)
5. É uma dor que parece não ter fim. (It is a pain that seems to have no end.)