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

Yes

The word "cebola" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the first vowel "e" is typically pronounced more clearly and openly (as /seˈbola/). In Continental Portuguese, the "e" is often reduced or "weakened," sounding much more like a neutral schwa (/səˈbola/), and the rhythm of the word is more stress-timed compared to the syllable-timed rhythm often heard in Brazil.

Brazilian Portuguese Examples

1. Eu gosto de colocar cebola no meu sanduíche. (I like to put onion in my sandwich.)
2. Você comprou cebola no mercado hoje? (Did you buy onion at the market today?)
3. Eu estou cortando a cebola para o refogado. (I am cutting the onion for the sauté.)
4. Tem muita cebola nessa salada. (There is a lot of onion in this salad.)
5. Eu não suporto o cheiro de cebola crua. (I can't stand the smell of raw onion.)

Continental Portuguese Examples

1. Eu gosto de pôr cebola no meu sanduíche. (I like to put onion in my sandwich.)
2. Compraste cebola no mercado hoje? (Did you buy onion at the market today?)
3. Estou a cortar a cebola para o refogado. (I am cutting the onion for the sauté.)
4. Há muita cebola nesta salada. (There is a lot of onion in this salad.)
5. Não suporto o cheiro de cebola crua. (I can't stand the smell of raw onion.)