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

Yes

The meaning, spelling, and grammar of "desistir" are identical in both Brazilian and European Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open, and the "s" in "desistir" is pronounced as a /z/ sound. In European Portuguese, vowels are often reduced or shortened, and the "s" before a consonant is typically pronounced as a "sh" sound (/ʃ/).

Brazilian Portuguese Examples

1. Eu não vou desistir dos meus sonhos. (I am not going to give up on my dreams.)
2. Ele desistiu de jogar futebol. (He gave up playing soccer.)
3. Não desista agora, você está quase lá! (Don't give up now, you are almost there!)
4. Ela desistiu do emprego para cuidar do filho. (She quit her job to take care of her child.)
5. A gente não pode desistir desse projeto. (We can't give up on this project.)

European Portuguese Examples

1. Eu não vou desistir dos meus sonhos. (I am not going to give up on my dreams.)
2. Ele desistiu de jogar futebol. (He gave up playing soccer.)
3. Não desistas agora, estás quase lá! (Don't give up now, you are almost there!)
4. Ela desistiu do emprego para cuidar do filho. (She quit her job to take care of her child.)
5. Nós não podemos desistir deste projeto. (We cannot give up on this project.)