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

Yes

The word "véspera" has the exact same meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. It refers to the day or the period immediately preceding a specific event (the "eve" or "the day before"). The only differences are phonetic; Brazilian Portuguese tends to pronounce unstressed vowels with more openness, whereas Continental Portuguese often reduces or "closes" unstressed vowels, making the word sound slightly more clipped or neutralized.

Brazilian Portuguese Examples

1. Eu estava muito nervoso na véspera da prova. (I was very nervous on the eve of the exam.)
2. A festa vai ser na véspera de Natal. (The party is going to be on Christmas Eve.)
3. Eles chegaram na véspera do feriado. (They arrived on the day before the holiday.)
4. Tudo estava pronto na véspera do casamento. (Everything was ready on the eve of the wedding.)
5. Eu não consigo dormir na véspera de uma viagem. (I can't sleep the night before a trip.)

Continental Portuguese Examples

1. Eu estava bastante ansioso na véspera do exame. (I was quite anxious on the eve of the exam.)
2. A celebração ocorre na véspera de Natal. (The celebration takes place on Christmas Eve.)
3. Eles chegaram na véspera do feriado. (They arrived on the day before the holiday.)
4. Tudo estava organizado na véspera do evento. (Everything was organized on the eve of the event.)
5. Não dormi nada na véspera da viagem. (I didn't sleep at all the night before the trip.)