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

No.

The difference lies in typical usage. While the literal meaning of "percebi" (I noticed/perceived) is identical in both dialects, the scope of the verb perceber differs significantly. In Brazil, "percebi" is primarily used for "noticing" or "realizing" a sensory or subtle change; for cognitive comprehension (understanding), Brazilians much more frequently use the verb entender. In Portugal, "perceber" is the standard, everyday verb used to mean "to understand" (e.g., "Não percebi" = "I didn't understand").

Brazilian Portuguese

1. Percebi que você estava triste. (I noticed you were sad.)
2. Percebi o erro no relatório. (I noticed the error in the report.)
3. Percebi que ele estava mentindo. (I noticed he was lying.)
4. Percebi que o café estava frio. (I noticed that the coffee was cold.)
5. Percebi que a porta estava aberta. (I noticed that the door was open.)

European Portuguese

1. Não percebi o que o professor explicou. (I didn't understand what the teacher explained.)
2. Percebi a tua mensagem. (I understood your message.)
3. Tu percebeste o que eu disse? (Did you understand what I said?)
4. Não percebi nada desta aula. (I didn't understand anything of this class.)
5. Percebi o teu ponto de vista. (I understood your point of view.)