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

Yes

The differences between the use of "justo" in Brazilian and Continental Portuguese are strictly phonetic. In Brazilian Portuguese, the pronunciation tends to be more "syllable-timed," with more open and clearly articulated vowels. In Continental Portuguese, the pronunciation is more "stress-timed," and unstressed vowels (such as the final 'o') are often heavily reduced, making them sound more like a short "u" or even nearly disappearing in rapid speech. There are no differences in spelling, grammar, or the fundamental meaning of the word.

Brazilian Portuguese Examples

1. Ele é um juiz muito justo. (He is a very just judge.)
2. O preço desse carro é justo. (The price of that car is fair.)
3. Isso aconteceu justo quando eu ia sair. (That happened just when I was about to leave.)
4. Essa calça tá muito justa em você. (Those pants are very tight on you.)
5. O valor é justo para o trabalho feito. (The value is fair for the work done.)

Continental Portuguese Examples

1. Ele é um homem justo. (He is a just man.)
2. O preço parece-me justo. (The price seems fair to me.)
3. Chegou justo a tempo do comboio. (He arrived just in time for the train.)
4. A camisola está demasiado justa. (The sweater is too tight.)
5. É um argumento justo. (It is a fair argument.)