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

Yes

The spelling, meaning, and grammatical function of "asiáticos" are identical in both Brazilian and European Portuguese. The only differences are phonological. In Brazilian Portuguese, the vowels are generally more open and clearly articulated, and in many Brazilian regions, the "ti" syllable may undergo palatalization (sounding like "tchee"). In European Portuguese, vowels in unstressed syllables are often "reduced" or almost swallowed, and the "t" remains a dental sound.

Brazilian Portuguese Examples

1. Muitos asiáticos moram no Brasil. (Many Asians live in Brazil.)
2. Os restaurantes asiáticos são ótimos. (Asian restaurants are great.)
3. Ele tem muitos amigos asiáticos. (He has many Asian friends.)
4. Os produtos asiáticos são bem baratos. (Asian products are very cheap.)
5. Os povos asiáticos têm histórias incríveis. (Asian peoples have incredible histories.)

European Portuguese Examples

1. Há muitos asiáticos a viver em Portugal. (There are many Asians living in Portugal.)
2. Os pratos asiáticos são excelentes. (Asian dishes are excellent.)
3. Ele tem vários amigos asiáticos. (He has several Asian friends.)
4. Os artigos asiáticos são muito baratos. (Asian goods are very cheap.)
5. Os povos asiáticos têm histórias incríveis. (Asian peoples have incredible histories.)