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

Yes

The word "inimigo" is identical in meaning, spelling, and grammar in both Brazilian and European Portuguese. The only difference lies in pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental (European) Portuguese, unstressed vowels are much more "closed" or reduced; for example, the initial "i" and the final "o" are often shortened or muffled, making the word sound more consonant-heavy to a non-native ear.

Brazilian Portuguese (Natural Usage)

1. Ele se tornou meu maior inimigo. (He became my greatest enemy.)
2. O medo é o nosso pior inimigo. (Fear is our worst enemy.)
3. Não faça dele o seu inimigo. (Don't make him your enemy.)
4. Eles são inimigos mortais. (They are mortal enemies.)
5. O tempo é um inimigo perigoso. (Time is a dangerous enemy.)

European Portuguese (Natural Expression)

1. Ele tornou-se o meu maior inimigo. (He became my greatest enemy.)
2. O medo é o nosso pior inimigo. (Fear is our worst enemy.)
3. Não o tornes o teu inimigo. (Don't make him your enemy.)
4. São inimigos mortais. (They are mortal enemies.)
5. O tempo é um inimigo perigoso. (Time is a dangerous enemy.)