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

Yes.

The word sozinho is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. Brazilian Portuguese tends to have more open, clearly articulated vowels, making the word sound more melodic and "syllable-timed." In Continental Portuguese, unstressed vowels undergo significant reduction; the "o" in the first syllable is often "swallowed" or reduced to a very short, nearly silent sound, making the word sound more clipped and consonant-heavy.

While the word itself does not change, the surrounding sentence structure used to express the same idea typically differs (such as the use of the gerund in Brazil versus the "a + infinitive" in Portugal).

Brazilian Portuguese Examples

1. Eu estou sozinho em casa. (I am alone at home.) *2. Você gosta de viajar sozinho? (Do you like traveling alone?)
2. Ele está brincando sozinho no quarto. (He is playing alone in the room.)
3. Ela resolveu o problema sozinha. (She solved the problem by herself.)
4. Eu vou fazer o trabalho sozinho. (I am going to do the work alone.)

European Portuguese Examples

1. Eu estou sozinho em casa. (I am alone at home.)
2. Tu gostas de viajar sozinho? (Do you like traveling alone?)
3. Ele está a brincar sozinho no quarto. (He is playing alone in the room.)
4. Ela resolveu o problema sozinha. (She solved the problem by herself.)
5. Eu vou fazer o trabalho sozinho. (I am going to do the work alone.)