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

Yes

The word "hora" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only differences lie in pronunciation. In many Brazilian dialects, the "r" can be realized as a retroflex "r" (like the American English "r") or a guttural sound, and the vowels tend to be more open and clearly articulated. In Continental Portuguese, the "r" is typically an alveolar tap or trill, and the unstressed vowels are much more reduced or "clipped," making the word sound shorter and more neutralized.

Brazilian Portuguese Examples

1. Que horas são agora? (What time is it now?)
2. Já passou da hora de você ir dormir. (It is past the time for you to go to sleep.)
3. A gente se encontra na hora do almoço. (We will meet at lunchtime.)
4. Não tenho uma hora livre hoje à tarde. (I don't have one free hour this afternoon.)
5. Na hora de pagar, ele percebeu que esqueceu a carteira. (At the moment of paying, he realized he forgot his wallet.)

Continental Portuguese Examples

1. Que horas são agora? (What time is it now?)
2. Já passou da hora de ires dormir. (It is past the time for you to go to sleep.)
3. Encontramo-nos na hora do almoço. (We will meet at lunchtime.)
4. Não tenho uma hora livre hoje à tarde. (I don't have one free hour this afternoon.)
5. Na hora de pagar, ele reparou que se tinha esquecido da carteira. (At the moment of paying, he noticed that he had forgotten his wallet.)