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

Yes

The word "controvertido" is identical in meaning, spelling, and grammatical classification in both Brazilian and Continental Portuguese. The only differences lie in how the word is pronounced and how it interacts with the surrounding sentence structure:

• Pronunciation: Brazilian Portuguese tends to have more open vowels and a more melodic, syllable-timed rhythm. Continental Portuguese features much more frequent vowel reduction (where unstressed vowels are "swallowed" or almost silent) and a more stress-timed rhythm. Additionally, the "s" in many positions is pronounced with a more distinct "sh" ([ʃ]) sound in Portugal.
• Syntactic Environment: While the word's properties remain unchanged, the grammar of the sentences containing it varies by dialect. A Brazilian would typically use the gerund (e.g., está sendo) and proclisis (e.g., ele se envolveu), whereas a Portuguese person would naturally use the preposition + infinitive (e.g., está a ser) and enclisis (e.g., ele envolveu-se).

Brazilian Portuguese Examples

1. Esse assunto é muito controvertido no Brasil. (This subject is very controversial in Brazil.)
2. A decisão do juiz foi bastante controvertida. (The judge's decision was quite controversial.)
3. O uso de IA está sendo um tema controvertido. (The use of AI is being a controversial theme.)
4. Ele se envolveu em uma discussão controvertida. (He got involved in a controversial discussion.)
5. Existe um entendimento controvertido sobre essa lei. (There is a controversial understanding about this law.)

Continental Portuguese Examples

1. Este assunto é muito controvertido em Portugal. (This subject is very controversial in Portugal.)
2. A decisão do juiz foi bastante controvertida. (The judge's decision was quite controversial.)
3. O uso de IA está a ser um tema controvertido. (The use of AI is being a controversial theme.)
4. Ele envolveu-se numa discussão controvertida. (He got involved in a controversial discussion.)
5. Existe um entendimento controvertido sobre esta lei. (There is a controversial understanding about this law.)