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

Yes

The meaning, spelling, and grammatical function of "perdido" are identical in both Brazilian and Continental Portuguese. It is the past participle of the verb perder (to lose) and can be used to describe something that is physically lost, someone who is lost in a location, or someone who is confused/clueless.

The only difference is pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated (e.g., per-DI-du). In Continental Portuguese, unstressed vowels are often "reduced" or shortened, making the word sound much more clipped and the "e" almost silent (e.g., p'r-DI-du).

Brazilian Portuguese Examples

1. Eu perdi meu celular e agora estou perdido sem o GPS. (I lost my cell phone and now I am lost without GPS.)
2. O cachorro perdido foi encontrado pelo vizinho. (The lost dog was found by the neighbor.)
3. O menino ficou perdido no shopping. (The boy got lost in the mall.)
4. Estou meio perdido nessa matéria da escola. (I am a bit lost in this school subject.)
5. Ele parece um pouco perdido com tantas mudanças. (He seems a little lost with so many changes.)

Continental Portuguese Examples

1. Perdi o meu telemóvel e agora estou perdido sem o GPS. (I lost my mobile phone and now I am lost without GPS.)
2. O cão perdido foi encontrado pelo vizinho. (The lost dog was found by the neighbor.)
3. A criança ficou perdida no centro comercial. (The child got lost in the shopping center.)
4. Estou um bocado perdido com esta disciplina. (I am a bit lost with this subject.)
5. Ele parece um pouco perdido com tantas alterações. (He seems a little lost with so many changes.)