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

Yes

The word "embora" is identical in both Brazilian and Continental Portuguese regarding its meaning, spelling, and grammatical function. It serves two primary roles in both dialects: as a concessive conjunction (meaning "although" or "even though") and as an adverb used in the verbal expression "ir embora" (meaning "to leave" or "to go away"). The only differences are in pronunciation (the Brazilian accent typically uses more open vowels, while the Portuguese accent is more closed and reduced) and the syntactic context (how the word interacts with other regional grammar structures, such as the gerund in Brazil versus the "a + infinitive" construction in Portugal).

Brazilian Portuguese Examples:

1. Embora esteja chovendo, eu vou sair. (Although it is raining, I am going out.)
2. Eu preciso ir embora agora. (I need to leave now.)
3. Embora ele seja rico, ele é muito simples. (Although he is rich, he is very simple.)
4. Vá embora daqui! (Go away from here!)
5. A gente vai embora logo. (We are leaving soon.)

Continental Portuguese Examples:

1. Embora esteja a chover, eu vou sair. (Although it is raining, I am going out.)
2. Eu preciso de ir embora agora. (I need to leave now.)
3. Embora ele seja rico, ele é muito simples. (Although he is rich, he is very simple.)
4. Vai-te embora daqui! (Go away from here!)
5. Nós vamos embora logo. (We are leaving soon.)