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

No.

While the definition and spelling are identical, there are differences in typical usage (register) and grammar (conjugation). In Brazil, "julgar" is frequently used in a more casual or mid-register sense to mean "to think" or "to consider." In Portugal, "julgar" carries a much more formal tone; for a simple opinion, a Portuguese person would more naturally use "achar" or "crer." Additionally, because the second-person (tu) is much more prevalent in informal Portuguese, the conjugation of the imperative and the second-person forms differs from the Brazilian preference for você.

Brazilian Portuguese Examples

1. Não julgue as pessoas pela aparência. (Don't judge people by appearance.)
2. Eu julgo que essa é a melhor opção. (I think this is the best option.)
3. O juiz vai julgar o caso hoje. (The judge will judge the case today.)
4. Você não deve julgar o que não conhece. (You shouldn't judge what you don't know.)
5. Eu julgo que ele está sendo sincero. (I think he is being sincere.)

Continental Portuguese Examples

1. Não julgues as pessoas pela aparência. (Don't judge people by appearance.)
2. Acho que esta é a melhor opção. (I think this is the best option.)
3. O juiz vai julgar o processo hoje. (The judge will judge the case today.)
4. Tu não deves julgar o que não conheces. (You shouldn't judge what you don't know.)
5. Creio que ele esteja a ser sincero. (I believe he is being sincere.)