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

Yes

The meaning, grammar, and spelling of "sobretudo" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the unstressed vowels are generally more open and clearly articulated. In Continental Portuguese, there is a significant reduction of unstressed vowels; the "e" in "sobre" is often neutralized or reduced to a near-silent sound, making the word sound more compressed and "clipped" compared to the Brazilian pronunciation.

Brazilian Portuguese Examples

1. Ela gosta de frutas, sobretudo de maçã. (She likes fruits, especially apples.)
2. O rapaz estava usando um sobretudo preto. (The boy was wearing a black overcoat.)
3. Precisamos de atenção, sobretudo com a segurança. (We need attention, especially regarding safety.)
4. Ele é muito inteligente, sobretudo em matemática. (He is very intelligent, especially in math.)
5. Onde você comprou esse sobretudo? (Where did you buy this overcoat?)

Continental Portuguese Examples

1. Ela gosta de fruta, sobretudo de maçã. (She likes fruit, especially apples.)
2. O rapaz estava a usar um sobretudo preto. (The boy was wearing a black overcoat.)
3. Precisamos de atenção, sobretudo no que toca à segurança. (We need attention, especially regarding safety.)
4. Ele é muito inteligente, sobretudo em matemática. (He is very intelligent, especially in math.)
5. Onde é que compraste esse sobretudo? (Where did you buy that overcoat?)