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

Yes

The meaning, grammar, and spelling of "superar" are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more "open" and the rhythm is more melodic (syllable-timed). In Continental Portuguese, unstressed vowels are often "reduced" or almost silent, creating a more "stress-timed" rhythm where the word sounds more clipped.

Brazilian Portuguese Examples

1. Você superou todos os obstáculos do caminho. (You overcame all the obstacles in the way.)
2. O resultado da prova superou as minhas expectativas. (The exam result exceeded my expectations.)
3. Ela está tentando superar esse trauma. (She is trying to get over this trauma.)
4. É preciso superar o medo para crescer. (It is necessary to overcome fear to grow.)
5. O atleta superou o recorde mundial de natação. (The athlete surpassed the world swimming record.)

Continental Portuguese Examples

1. Tu superaste todos os obstáculos do caminho. (You overcame all the obstacles in the way.) Note: In Portugal, the second person "tu" is used much more naturally for direct address.
2. O resultado do exame superou as minhas expectativas. (The exam result exceeded my expectations.) Note: "Exame" is more commonly used in Portugal than "prova" for formal tests.
3. Ela está a tentar superar esse trauma. (She is trying to get over this trauma.) Note: Portuguese people use the "a + infinitive" construction instead of the Brazilian gerund ("está tentando").
4. É preciso superar o medo para crescer. (It is necessary to overcome fear to grow.)
5. O atleta superou o recorde mundial de natação. (The athlete surpassed the world swimming record.)