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

No

While the core dictionary definitions are the same, there is a significant difference in typical usage and connotation. In Brazil, "estar comprometido" is a very common, everyday way to say someone is "taken" or "in a relationship" (not single). In Portugal, using "comprometido" to describe a romantic relationship sounds much more formal and often specifically implies a legal or marriage-bound engagement (noivado). Additionally, in Portugal, the word is more frequently used to mean "implicated" in a scandal or legal matter.

Brazilian Portuguese Examples

1. Ele é um funcionário muito comprometido. (He is a very committed employee.)
2. Não posso sair hoje, estou comprometido. (I can't go out today, I'm in a relationship/taken.)
3. A saúde dele está muito comprometida. (His health is very compromised/at risk.)
4. O orçamento da empresa está comprometido. (The company's budget is committed/allocated.)
5. Ela é uma pessoa muito comprometida com a causa. (She is a person very committed to the cause.)

Portuguese (Portugal) Examples

1. Ele é um colaborador muito dedicado. (He is a very dedicated employee.)
2. Não posso sair hoje, estou num relacionamento. (I can't go out today, I'm in a relationship.)
3. A saúde dele está muito debilitada. (His health is very debilitated/weakened.)
4. O orçamento da empresa está comprometido. (The company's budget is committed/allocated.)
5. Ela é uma pessoa muito empenhada na causa. (She is a person very dedicated/engaged to the cause.)