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

Yes

The spelling, meaning, and grammatical function of "quatro" are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are more open and clearly articulated. In Continental Portuguese, the vowels are more "closed" or reduced, which often makes the word sound more clipped or swallowed.

Brazilian Portuguese Examples

1. Eu tenho quatro irmãos. (I have four brothers.)
2. São quatro horas da tarde. (It is four o'clock in the afternoon.)
3. Ele comprou quatro carros novos. (He bought four new cars.)
4. Eu quero quatro fatias de bolo. (I want four slices of cake.)
5. Tem quatro pessoas na sala. (There are four people in the room.)

Continental Portuguese Examples

1. Tenho quatro irmãos. (I have four brothers.)
2. São quatro horas da tarde. (It is four o'clock in the afternoon.)
3. Ele comprou quatro automóveis novos. (He bought four new cars.)
4. Quero quatro fatias de bolo. (I want four slices of cake.)
5. Há quatro pessoas na sala. (There are four people in the room.)