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

No.

While the core meaning and spelling of "gostar" remain the same in both dialects, there are significant differences in typical usage and pronunciation.

In terms of usage, the way "gostar" interacts with pronouns and subjects differs. Brazilians naturally use "você" (or the informal "te") and frequently use "a gente" to represent "we." In contrast, Portuguese people more commonly use "tu" (and the corresponding "ti") and "nós." Additionally, the grammatical environment changes; for example, the preposition used for "at/on the weekend" differs. In terms of pronunciation, Brazilian Portuguese is characterized by open, melodic vowels, whereas Continental Portuguese features heavy vowel reduction, where unstressed vowels are often shortened or almost swallowed entirely.

Brazilian Portuguese Examples

1. Eu gosto muito de chocolate. (I like chocolate a lot.)
2. Você gosta de viajar? (Do you like to travel?)
3. A gente gosta de sair no fim de semana. (We like to go out on the weekend.)
4. Eu gosto de você. (I like you.)
5. Eles gostam de jogar futebol. (They like playing soccer.)

Continental Portuguese Examples

1. Eu gosto muito de chocolate. (I like chocolate a lot.)
2. Tu gostas de viajar? (Do you like to travel?)
3. Nós gostamos de sair ao fim de semana. (We like to go out at the weekend.)
4. Eu gosto de ti. (I like you.)
5. Eles gostam de jogar futebol. (They like playing soccer.)