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

Yes

The meaning, grammar, and spelling of "vermelhos" are identical in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels tend to be more open and clearly articulated. In Continental Portuguese, unstressed vowels are often more closed or even reduced (often sounding almost swallowed), which changes the phonetic rhythm of the word.

Brazilian Portuguese

1. Os seus carros vermelhos são muito rápidos. (Your red cars are very fast.)
2. Eu gosto de detalhes vermelhos. (I like red details.)
3. Esses sapatos vermelhos são muito bonitos. (These red shoes are very beautiful.)
4. Os pássaros vermelhos são lindos. (The red birds are beautiful.)
5. Os brinquedos vermelhos estão no chão. (The red toys are on the floor.)

Continental Portuguese

1. Os teus carros vermelhos são muito rápidos. (Your red cars are very fast.)
2. Gosto de detalhes vermelhos. (I like red details.)
3. Estes sapatos vermelhos são muito giros. (These red shoes are very pretty.)
4. Os pássaros vermelhos são lindos. (The red birds are beautiful.)
5. Os brinquedos vermelhos estão no chão. (The red toys are on the floor.)