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

No.

While the spelling and dictionary meaning of "amigo" are identical in both dialects, there are significant differences in typical usage and pronimentation. In Brazil, "amigo" is frequently used as a casual, generic way to address strangers or people in service positions (e.g., "Oi, amigo"). In Portugal, using "amigo" to address a stranger is much less common and can be perceived as overly familiar or even disrespectful; a Portuguese person would typically use "senhor" or "moço" instead. Furthermore, the pronunciation differs: Brazilian Portuguese features more open, clear vowels, whereas Continental Portuguese features heavy vowel reduction, making unstressed vowels sound much more closed or almost neutralized.

Brazilian Portuguese Examples

1. "Oi, amigo, você viu meu ônibus?" (Hey, friend, did you see my bus?)
2. "Ele é meu amigo de infância." (He is my childhood friend.)
3. "Aquele amigo é muito legal." (That friend is very cool.)
4. "Meu amigo mora no Rio." (My friend lives in Rio.)
5. "E aí, amigo, beleza?" (Hey, friend, what's up?)

Continental Portuguese Examples

1. "Com licença, senhor, viu o meu autocarro?" (Excuse me, sir, did you see my bus?)
2. "Ele é o meu amigo de infância." (He is my childhood friend.)
3. "Aquele amigo é muito porreiro." (That friend is very cool.)
4. "O meu amigo vive no Rio." (My friend lives in Rio.)
5. "Olá, tudo bem?" (Hello, how are you?)