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

No.

While the core physical meaning of "bater" (to hit, to strike, or to knock) remains the same in both dialects, there are significant differences in typical usage and idiomatic expressions. In Brazilian Portuguese, "bateu" is frequently used metaphorically to describe the sudden onset of an emotion, a craving, or an impulse (e.g., "bateu uma vontade"). In Continental Portuguese, these abstract feelings are more naturally expressed using verbs like surgir (to arise) or dar (to give/to cause). Additionally, the preposition used with "bater" when referring to doors differs, and for vehicle accidents, Portuguese speakers often prefer chocar-se or colidir instead of bater.

Brazilian Portuguese Usage

1. Bateu uma saudade de casa. (A feeling of longing for home hit me.)
2. O carro bateu no poste. (The car hit the pole.)
3. Bateu um desânimo enorme depois da reunião. (A huge feeling of discouragement set in after the meeting.)
4. Ele bateu na minha porta. (He knocked on my door.)
5. Ele bateu o recorde de velocidade. (He broke the speed record.)

Continental Portuguese Usage

1. Senti muita saudade de casa. (I missed home a lot.)
2. O carro chocou-se contra o poste. (The car crashed into the pole.)
3. Fiquei com um desânimo enorme depois da reunião. (I became hugely discouraged after the meeting.)
4. Ele bateu à minha porta. (He knocked on my door.)
5. Ele superou o recorde de velocidade. (He surpassed the speed record.)