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

Yes

The word "cobra" is identical in spelling, meaning, and grammatical gender in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels tend to be more open, and the "r" is often realized as a retroflex or a soft alveolar tap depending on the region. In Continental Portuguese, the vowels are typically more closed, and the "r" is usually a more distinct, sharp alveolar tap or trill. While the word itself is the same, the surrounding syntax (the way sentences are built) often differs between the two varieties.

Brazilian Portuguese

1. Cuidado com aquela cobra no jardim! (Watch out for that snake in the garden!)
2. Ela é uma cobra, não confie nela. (She is a snake, don't trust her.)
3. Vi uma cobra pequena passando pelo mato. (I saw a small snake passing through the bushes.)
4. A cobra picou o pé do menino. (The snake bit the boy's foot.)
5. Não seja cobra com seus amigos. (Don't be a snake with your friends.)

Portuguese (Portugal)

1. Há uma cobra ali no jardim! (There is a snake there in the garden!)
2. Ela é uma cobra, não te fies nela. (She is a snake, don't trust her.)
3. Vi uma cobra a passar pelo mato. (I saw a snake passing through the bushes.)
4. A cobra picou o pé do rapaz. (The snake bit the boy's foot.)
5. Não sejas uma cobra com os teus amigos. (Don't be a snake with your friends.)