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

No.

The difference between the two dialects regarding this word is not in spelling or core meaning, but in grammatical usage (regência verbal). When "assistir" is used to mean "to watch," Brazilians naturally use it as a direct transitive verb, omitting the preposition. In Portugal, the standard and natural usage is as an indirect transitive verb, which requires the preposition "a" (often resulting in the use of contractions like ao or à).

Brazilian Portuguese Examples

1. Eu assistia muito desenho quando era criança. (I used to watch a lot of cartoons when I was a child.)
2. Ela assistia o jogo de futebol no estádio. (She used to watch the football match at the stadium.)
3. A gente assistia muita novela na TV. (We used to watch a lot of soap operas on TV.)
4. Ele assistia as notícias todo dia. (He used to watch the news every day.)
5. Nós assistíamos o filme com muita atenção. (We used to watch the movie with a lot of attention.)

European Portuguese Examples

1. Eu assistia muito a desenhos quando era criança. (I used to watch a lot of cartoons when I was a child.)
2. Ela assistia ao jogo de futebol no estádio. (She used to watch the football match at the stadium.)
3. Nós assistíamos à novela na TV. (We used to watch the soap opera on TV.)
4. Ele assistia às notícias todos os dias. (He used to watch the news every day.)
5. Nós assistíamos ao filme com muita atenção. (We used to watch the movie with a lot of attention.)