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

Yes

The only differences between the word "verdade" in Brazilian and Continental Portuguese are in pronunciation.

In Brazilian Portuguese, the final "e" is typically pronounced as an unstressed /i/ (like the "ee" in "see"), making the word sound like ver-DA-jee. In Continental Portuguese, unstressed vowels are heavily reduced or "swallowed." Consequently, the final "e" is often nearly silent or extremely short, making the word sound more like ver-DAHD. The meaning, spelling, and grammatical function of the word remain identical in both varieties.

Brazilian Portuguese Usage

1. "Me diga a verdade." (Tell me the truth.)
2. "É verdade, eu esqueci totalmente." (It's true, I totally forgot.)
3. "Você está falando a verdade?" (Are you telling the truth?)
4. "Isso não é verdade nem ferrando!" (That's not true, no way!)
5. "A verdade é que eu não sei." (The truth is that I don't know.)

Continental Portuguese Usage

1. "Diz-me a verdade." (Tell me the truth.)
2. "É verdade, eu esqueci-me completamente." (It's true, I completely forgot.)
3. "Estás a dizer a verdade?" (Are you telling the truth?)
4. "Isso não é verdade de maneira nenhuma!" (That's not true in any way!)
5. "A verdade é que eu não sei." (The truth is that I don't know.)