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

Yes

The word "passado" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels tend to be much more closed or even "reduced" (nearly swallowed). For "passado," a Portuguese person will pronounce the first "a" in a much more closed, neutral way (sounding almost like a very short, muffled "uh"), whereas a Brazilian will pronounce it with a clearer, more open "ah" sound.

Brazilian Portuguese Examples

1. Eu não gosto de falar do meu passado. (I don't like talking about my past.)
2. O que passou, passou. (What is past, is past.)
3. Ele tem um passado muito complicado. (He has a very complicated past.)
4. O tempo passado era muito mais simples. (The past time was much simpler.)
5. Não viva preso ao passado. (Don't live stuck in the past.)

Continental Portuguese Examples

1. Não gosto de falar do meu passado. (I don't like talking about my past.)
2. O que passou, passou. (What is past, is past.)
3. Ele tem um passado bastante complicado. (He has a quite complicated past.)
4. O tempo passado era bem mais simples. (The past time was much simpler.)
5. Não vivas preso ao passado. (Don't live stuck in the past.)