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

Yes.

The spelling, meaning, and grammatical gender of "universidade" are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In most Brazilian dialects, the "d" before the "e" is palatalized, sounding like "dji" (/dʒi/). In Continental Portuguese, the "d" is pronounced as a dental or alveolar consonant, similar to the "d" in the English word "did." Additionally, Brazilian Portuguese tends to have more open, resonant vowels, while European Portuguese features more closed or reduced vowel sounds.

Brazilian Portuguese Examples

1. Eu estudo na universidade de São Paulo. (I study at the University of São Paulo.)
2. A universidade é muito grande e moderna. (The university is very large and modern.)
3. Ela se formou na universidade ano passado. (She graduated from the university last year.)
4. Tem muita gente na universidade hoje. (There are many people at the university today.)
5. Você já fez a matrícula na universidade? (Have you already enrolled in the university?)

Continental Portuguese Examples

1. Estou a estudar na universidade de Coimbra. (I am studying at the University of Coimbra.)
2. A universidade fica perto de minha casa. (The university is near my house.)
3. Ela licenciou-se na universidade no ano passado. (She graduated from the university last year.)
4. É necessário investir mais na universidade. (It is necessary to invest more in the university.)
5. Já fiz a inscrição na universidade? (Have I already registered at the university?)