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

Yes

The word "competências" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels are often "reduced" or "closed," meaning they are spoken much more softly or are nearly swallowed in rapid speech (for example, the first 'e' in "competências" may sound almost like a silent or very short 'i' in Portugal).

Brazilian Portuguese Examples

1. Ela tem muitas competências técnicas. (She has many technical skills.)
2. O currículo mostra bem as suas competências. (The resume shows your skills well.)
3. A gente precisa desenvolver novas competências. (We need to develop new skills.)
4. Quais são as principais competências dele? (What are his main skills?)
5. Ele tem competências de liderança incríveis. (He has incredible leadership skills.)

Continental Portuguese Examples

1. Ela demonstra excelentes competências técnicas. (She demonstrates excellent technical skills.)
2. O currículo evidencia as suas competências. (The CV evidences your skills.)
3. É fundamental desenvolver novas competências. (It is fundamental to develop new skills.)
4. Que competências é que ele possui? (What skills does he possess?)
5. Ele detém competências de liderança fundamentais. (He holds fundamental leadership skills.)