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

No.

While the literal meaning (referring to weight or mass) is identical in both dialects, there is a difference in typical usage. In Brazilian Portuguese, "pesado" is used much more extensively as a slang term. In Brazil, it acts as a versatile adjective to describe anything intense, extreme, difficult, or even offensive/gross. In Portugal, while the word can be used to describe something rude or a difficult task, it is less frequently used as a general-purpose slang for "wild" or "intense," where other adjectives are more natural.

Brazilian Portuguese Examples

1. A música é muito pesada. (The music is very intense.)
2. Que comentário pesado! (What a rude/offensive comment!)
3. O treino foi pesado hoje. (The workout was tough today.)
4. A festa ontem foi pesada. (The party yesterday was wild.)
5. O clima ficou pesado após a discussão. (The atmosphere became tense after the argument.)

Portuguese (Portugal) Examples

1. A música é muito forte. (The music is very intense.)
2. Que comentário desagradável! (What an unpleasant comment!)
3. O treino foi muito duro hoje. (The workout was very hard today.)
4. A festa ontem foi muito agitada. (The party yesterday was very wild.)
5. O ambiente ficou tenso após a discussão. (The atmosphere became tense after the argument.)