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

No

While the spelling and basic meaning of "ei" (as an interjection) are identical in both dialects, their typical usage differs. In Brazil, "Ei" is a standard and frequent way to grab someone's attention or initiate a conversation. In Portugal, while "Ei" is understood, it is much more common and natural for speakers to use "Olha" (Look) or "Overt" (Listen) to achieve the same communicative effect.

Brazilian Portuguese

1. Ei, você esqueceu seu celular! (Hey, you forgot your cell phone!)
2. Ei, o que você está fazendo aí? (Hey, what are you doing there?)
3. Ei, não fala assim com ela! (Hey, don't talk to her like that!)
4. Ei, olha aquele avião! (Hey, look at that airplane!)
5. Ei, presta atenção no que eu digo! (Hey, pay attention to what I'm saying!)

Continental Portuguese

1. Olha, esqueceste-te do teu telemóvel! (Look, you forgot your mobile phone!)
2. Ouve, o que é que estás a fazer aí? (Listen, what are you doing there?)
3. Olha, não fales assim com ela! (Look, don't talk to her like that!)
4. Olha, vê aquele avião! (Look, see that airplane!)
5. Olha, presta atenção ao que eu digo! (Look, pay attention to what I'm saying!)