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

No

While the spelling, grammar, and core meaning (to grip or seize) are identical, there is a difference in typical usage. In Brazilian Portuguese, "agarrar" is frequently used informally to mean "to catch" something, such as a bus or an illness. In Continental Portuguese, while "agarrar" is used for the physical act of gripping, the verb apanhar is the standard and much more natural choice for the concept of "catching" transport, objects, or diseases.

Brazilian Portuguese Examples

1. Ele agarrou a minha mão. (He grabbed my hand.)
2. O menino agarrou o brinquedo. (The boy grabbed the toy.)
3. Ele agarrou uma gripe. (He caught a flu.)
4. O jogador agarrou a bola. (The player caught the ball.)
5. Ela agarrou o ônibus. (She caught the bus.)

Continental Portuguese Examples

1. Ele agarrou-me a mão. (He grabbed my hand.)
2. O rapaz agarrou o brinquedo. (The boy grabbed the toy.)
3. Ele apanhou uma constipação. (He caught a cold.)
4. O guarda-redes apanhou a bola. (The goalkeeper caught the ball.)
5. Ela apanhou o autocarro. (She caught the bus.)