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

Yes

The only difference between the two variants is pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In European Portuguese, the rhythm is more "stress-timed," meaning unstressed vowels (such as the "e" in the second syllable of ausência) are often reduced, shortened, or almost swallowed, making the word sound more closed and clipped.

Brazilian Portuguese examples:

1. A ausência dele na aula foi justificada. (His absence from class was justified.)
2. A ausência de funcionários é um problema. (The absence of employees is a problem.)
3. A ausência de clareza gerou muitas dúvidas. (The absence of clarity caused many doubts.)
4. A ausência de sinais de vida é assustadora. (The absence of signs of life is scary.)
5. A ausência de provas é preocupante. (The absence of evidence is worrying.)

European Portuguese examples:

1. A falta dele na aula foi justificada. (His absence from class was justified.)
2. A ausência de funcionários é um problema. (The absence of employees is a problem.)
3. A falta de clareza gerou muitas dúvidas. (The lack of clarity caused many doubts.)
4. A ausência de sinais de vida é assustadora. (The absence of signs of life is scary.)
5. A falta de provas é preocupante. (The lack of evidence is worrying.)