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

No.

While the spelling and meaning of "conhece" (the third-person singular of the verb conhecer) are identical in both dialects, the typical usage and pronunciation differ significantly:

• Usage and Grammar: In Brazil, "conhece" is the standard form used with the pronoun você for almost all informal and semi-formal social interactions. In Portugal, "conhece" is used for formal or polite address, whereas informal address requires the second-person singular tu (which uses the form conheces). Additionally, Brazilians typically use subject pronouns as direct objects (e.g., "conhece ele"), whereas Portuguese people use enclitic pronouns (e.g., "conhece-o").
• Pronunciation: Brazilian Portuguese is generally more "open" and melodic, with clearly pronounced vowels. Continental Portuguese is more "stress-timed," meaning unstressed vowels (like the final 'e' in conhece) are often much more closed, reduced, or even swallowed.

Brazilian Portuguese Examples:

1. Você conhece o João? (Do you know João?)
2. Você conhece ele? (Do you know him?)
3. Você conhece esse lugar? (Do you know this place?)
4. Ele conhece todo mundo. (He knows everyone.)
5. Você conhece algum restaurante bom? (Do you know any good restaurant?)

Portuguese (Continental) Examples:

1. Tu conheces o João? (Do you know João?)
2. Conhece-o? (Do you know him?)
3. Tu conheces este sítio? (Do you know this place?)
4. Ele conhece toda a gente. (He knows everyone.)
5. Conheces algum restaurante por aqui? (Do you know any restaurant around here?)