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

Yes

The word "adora" (the third-person singular present indicative of the verb adorar) is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels tend to be "reduced" or "closed"; consequently, the "o" in "adora" may sound much shorter or more muffled to an untrained ear.

Brazilian Portuguese Examples

1. Ela adora comer pizza de madrugada. (She loves eating pizza in the middle of the night.)
2. O meu cachorro adora brincar no parque. (My dog loves playing in the park.)
3. Ele adora assistir a filmes de ação. (He loves watching action movies.)
4. Ela adora sair com os amigos no fim de semana. (She loves going out with friends on the weekend.)
5. Ele adora usar o celular novo. (He loves using his new cell phone.)

Portuguese (Continental) Examples

1. Ela adora comer pizza de madrugada. (She loves eating pizza in the middle of the night.)
2. O meu cão adora brincar no parque. (My dog loves playing in the park.)
3. Ele adora ver filmes de ação. (He loves watching action movies.)
4. Ela adora sair com os amigos ao fim de semana. (She loves going out with friends on the weekend.)
5. Ele adora usar o telemóvel novo. (He loves using his new mobile phone.)