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

No.

While the spelling and conjugation of "assistem" are identical in both dialects, the answer is No due to a difference in typical usage and grammar (verbal regency).

The difference specifically applies when the verb assistir means "to watch" or "to attend":

• Brazilian Portuguese: In natural, everyday speech, the verb is frequently used as a transitive direct verb, meaning the preposition "a" is often omitted (e.g., assistir o filme).
• Continental Portuguese: The verb is strictly used as a transitive indirect verb, meaning the preposition "a" is mandatory (e.g., assistir ao filme).

Note: When the verb means "to help/aid" (e.g., "to assist a patient"), the usage is the same in both dialects.

Brazilian Portuguese

1. Eles assistem o filme agora. (They are watching the movie now.)
2. As crianças assistem o desenho na TV. (The children are watching the cartoon on TV.)
3. Eles assistem o jogo no estádio. (They are watching the game at the stadium.)
4. Os médicos assistem os pacientes no hospital. (The doctors are assisting the patients in the hospital.)
5. Esses direitos assistem o trabalhador. (These rights protect the worker.)

Continental Portuguese

1. Eles assistem ao filme agora. (They are watching the movie now.)
2. As crianças assistem ao desenho na TV. (The children are watching the cartoon on TV.)
3. Eles assistem ao jogo no estádio. (They are watching the game at the stadium.)
4. Os médicos assistem os doentes no hospital. (The doctors are assisting the patients in the hospital.)
5. Esses direitos assistem ao trabalhador. (These rights protect the worker.)