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

No.

While the spelling and fundamental definition of "ouvir" are the same in both dialects, there are differences in typical usage, grammar, and pronunciation. In Brazil, "ouvir" is commonly used for both the passive act of hearing (perceiving sound) and the active act of listening (paying attention). In Portugal, "ouvir" is more strictly associated with the perception of sound, while "escutar" is the preferred word for the intentional act of listening. Additionally, there are grammatical differences in how verbs are conjugated in the past tense and how the present continuous is formed, as well as significant differences in pronunciation (specifically the realization of the final "r" and vowel quality).

Brazilian Portuguese Examples

1. Eu ouvi uma música ótima no rádio. (I heard/listened to a great song on the radio.)
2. Você pode ouvir o que eu estou falando? (Can you hear/listen to what I am saying?)
3. Eu ouvi um barulho na cozinha. (I heard a noise in the kitchen.)
4. A gente ouviu a explicação do professor. (We heard/listened to the teacher's explanation.)
5. Você ouviu falar do novo restaurante? (Have you heard about the new restaurant?)

Continental Portuguese Examples

1. Eu escutei uma música ótima no rádio. (I listened to a great song on the radio.)
2. Podes escutar o que eu estou a dizer? (Can you listen to what I am saying?)
3. Eu ouvi um ruído na cozinha. (I heard a noise in the kitchen.)
4. Nós escutámos a explicação do professor. (We listened to the teacher's explanation.)
5. Ouviste falar do novo restaurante? (Did you hear about the new restaurant?)