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

Yes.

The word "preste" is the third-person singular present subjunctive of the verb prestar. There are no differences in meaning, grammar, or spelling between Brazilian and Continental Portuguese. The only difference is in pronunciation:

• In Brazilian Portuguese, the final "e" is typically pronounced as a high, unrounded vowel [i], similar to the "ee" in "see" (e.g., pres-chee).
• In Continental Portuguese, the final "e" is an unstressed, reduced vowel, often sounding like a muffled [ə] or even becoming nearly silent (e.g., presht).

Brazilian Portuguese Examples

1. Espero que ele preste atenção na aula. (I hope he pays attention to the class.)
2. Não quero que ele preste o depoimento hoje. (I don't want him to give the testimony today.)
3. É importante que a empresa preste um bom serviço. (It is important that the company provides a good service.)
4. Peça para ele que preste cuidado com as crianças. (Ask him to be careful with the children.)
5. É necessário que ele preste contas do que gastou. (It is necessary that he accounts for what he spent.)

Continental Portuguese Examples

1. Espero que ele preste atenção à aula. (I hope he pays attention to the class.)
2. Não quero que ele preste o depoimento hoje. (I don't want him to give the testimony today.)
3. É importante que a empresa preste um bom serviço. (It is important that the company provides a good service.)
4. Diz-lhe que preste cuidado com as crianças. (Tell him to be careful with the children.)
5. É necessário que ele preste contas do que gastou. (It is necessary that he accounts for what he spent.)