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

No.

While the core meaning of "agora" (now) is identical, there are differences in typical usage and pronunciation. In Brazil, "agora" is frequently used in the expression "agora pouco" to refer to the recent past (meaning "a little while ago"), whereas in Portugal, the preposition "há" is the standard ("há pouco"). Furthermore, Brazilians often use "agora" to imply "from now on," while Portuguese speakers typically use the phrase "a partir de agora." Finally, the pronunciation differs significantly, as European Portuguese involves much more vowel reduction and closed sounds than Brazilian Portuguese.

Brazilian Portuguese

1. Agora eu vou dormir. (Now I am going to sleep.)
2. Você pode falar agora? (Can you talk now?)
3. Eu vi ele agora pouco. (I saw him a little while ago.)
4. Agora você é meu amigo. (From now on, you are my friend.)
5. Agora vai dar certo. (Now it is going to work.)

Continental Portuguese

1. Agora vou dormir. (Now I am going to sleep.)
2. Podes falar agora? (Can you talk now?)
3. Eu vi-o há pouco. (I saw him a little while ago.)
4. A partir de agora, és meu amigo. (From now on, you are my friend.)
5. Agora é que é! (This is it!)