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

No.

While the spelling and core definition of "estudo" (referring to the act of studying or a research paper) are identical in both dialects, there are significant differences in pronunciation and typical usage.

• Pronunciation: In Brazilian Portuguese, the initial "e" is typically an open or mid-vowel ([e]). In European Portuguese, due to heavy vowel reduction, the "e" is much more closed and central ([ɨ]), making it sound nearly like a very short "i" to English speakers.
• Usage: In Brazil, "estudo" is commonly used to refer to a person's level of education or schooling (e.g., "Ele tem pouco estudo"). In Portugal, while the meaning is understood, it is much more natural to use terms like "instrução" or "escolaridade" to describe this.

Brazilian Portuguese Examples

1. Eu estudo muito para o vestibular. (I study a lot for the university entrance exam.)
2. Ele tem pouco estudo. (He has little education.)
3. O meu estudo de caso foi nota dez. (My case study was a ten/perfect.)
4. O estudo da língua portuguesa é muito legal. (The study of the Portuguese language is very cool.)
5. Fiz um estudo de mercado para a empresa. (I did a market study for the company.)

European Portuguese Examples

1. Eu estudo muito para os exames. (I study a lot for the exams.)
2. Ele tem pouca instrução. (He has little education.)
3. O meu estudo de caso foi excelente. (My case study was excellent.)
4. O estudo da língua portuguesa é muito interessante. (The study of the Portuguese language is very interesting.)
5. Fiz um estudo de mercado para a empresa. (I did a market study for the company.)