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

Yes

The word "mudou" is identical in Brazilian and Continental Portuguese in terms of spelling, grammar, and core meaning (it is the third-person singular of the verb mudar in the pretérito perfeito). The only difference lies in pronunciation. In Brazilian Portuguese, the vowels tend to be more open and clearly articulated. In Continental Portuguese, vowels—especially unstressed ones—are often more "reduced" or clipped, making the pronunciation slightly more subtle or "tighter."

Brazilian Portuguese Examples

1. O clima mudou muito hoje. (The weather changed a lot today.)
2. Ele mudou de ideia na última hora. (He changed his mind at the last minute.)
3. A cidade mudou bastante nos últimos anos. (The city has changed a lot in recent years.)
4. Ela mudou de emprego para ganhar mais. (She changed jobs to earn more.)
5. O plano mudou por causa da chuva. (The plan changed because of the rain.)

Continental Portuguese Examples

1. O tempo mudou imenso. (The weather changed immensely.)
2. Ele mudou de opinião após a conversa. (He changed his opinion after the conversation.)
3. A freguesia mudou muito com a nova obra. (The parish changed a lot with the new construction.)
4. A política mudou após as eleições. (The policy changed after the elections.)
5. O plano mudou devido ao imprevisto. (The plan changed due to the unforeseen.)