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

Yes.

The word "mochila" is identical in spelling, meaning, and grammatical function in both Brazilian and European Portuguese. The only difference is pronunciation: Brazilians tend to pronounce the unstressed vowels with a more "open" or distinct sound, whereas in Portugal, these vowels are often more "closed" or reduced (a phonetic phenomenon known as vowel reduction).

Brazilian Portuguese Examples

1. Eu esqueci minha mochila no ônibus. (I forgot my backpack on the bus.)
2. Sua mochila está muito pesada. (Your backpack is very heavy.)
3. Vou colocar os lanches na mochila. (I'm going to put the snacks in the backpack.)
4. Onde você comprou essa mochila? (Where did you buy that backpack?)
5. A mochila dele é azul. (His backpack is blue.)

European Portuguese Examples

1. Esqueci-me da minha mochila no autocarro. (I forgot my backpack on the bus.)
2. A tua mochila está muito pesada. (Your backpack is very heavy.)
3. Vou pôr os lanches na mochila. (I'm going to put the snacks in the backpack.)
4. Onde é que compraste essa mochila? (Where did you buy that backpack?)
5. A mochila dele é azul. (His backpack is blue.)