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

No

While the primary meaning of "assistir" (to watch/to view) is the same in both varieties, there is a significant difference in grammar (specifically verb government/regência verbal) and typical usage.

• Grammar (Transitivity): In Continental Portuguese, "assistir" (when meaning to watch) is strictly a transitive indirect verb, meaning it must be followed by the preposition "a" (e.g., assistir ao filme). In Brazilian Portuguese, while the preposition is technically correct in formal writing, it is extremely common in spoken and informal Brazilian Portuguese to use it as a transitive direct verb, dropping the "a" (e.g., assistir o filme).
• Usage (Meaning "to help"): In Brazil, the word "ajudar" is the standard, everyday word for "to help." While "assistir" can mean "to assist" in Brazil, it is reserved for much more formal, medical, or legal contexts. In Portugal, "assistir" is more commonly used to denote providing professional assistance or care.

Brazilian Portuguese Examples (Natural/Informal usage)

1. Eu assisti o filme ontem à noite. (I watched the movie last night.)
2. Vamos assistir o jogo de futebol? (Shall we watch the soccer game?)
3. Ela adora assistir desenho animado. (She loves to watch cartoons.)
4. Você assistiu o documentário que eu te mandei? (Did you watch the documentary I sent you?)
5. A gente assistiu o jornal agora pouco. (We watched the news a little while ago.)

Continental Portuguese Examples (Natural/Standard usage)

1. Eu assisti ao filme ontem à noite. (I watched the movie last night.)
2. Vamos assistir ao jogo de futebol? (Shall we watch the soccer game?)
3. Ela adora assistir a desenhos animados. (She loves to watch cartoons.)
4. Tu assististe ao documentário que te enviei? (Did you watch the documentary I sent you?)
5. Nós assistimos ao telejornal agora mesmo. (We watched the news just now.)