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

No.

While the spelling and the core definition of "escutar" are the same in both varieties, there is a difference in typical usage. In Brazilian Portuguese, "escutar" is frequently used as a synonym for "ouvir" (to hear), and the distinction between the two is often blurred in casual conversation. In Continental Portuguese, "ouvir" is the much more common and preferred verb for both the act of hearing and the act of listening, whereas "escutar" is more strictly reserved for the intentional, active effort of paying attention.

Brazilian Portuguese usage:

1. Eu gosto de escutar música no meu quarto. (I like to listen to music in my room.)
2. Você está escutando o que eu estou falando? (Are you listening to what I am saying?)
3. Ele estava escutando um podcast no ônibus. (He was listening to a podcast on the bus.)
4. Escute bem essa explicação para não esquecer. (Listen well to this explanation so you don't forget.)
5. Nós gostamos de escutar o barulho do mar. (We like to listen to the sound of the sea.)

Continental Portuguese usage:

1. Eu gosto de ouvir música no meu quarto. (I like to listen to music in my room.)
2. Estás a ouvir o que eu estou a dizer? (Are you listening to what I am saying?)
3. Ele estava a ouvir um podcast no autocarro. (He was listening to a podcast on the bus.)
4. Ouve bem esta explicação para não te esqueceres. (Listen well to this explanation so you don't forget.)
5. Nós gostamos de ouvir o barulho do mar. (We like to listen to the sound of the sea.)