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

No.

While the meaning and spelling of "consigo" are identical in both varieties of Portuguese, there is a significant difference in typical usage (register). In Brazilian Portuguese, "consigo" is considered a high-register, formal, or literary word. It is rarely used in everyday spoken conversation, where Brazilians much prefer using "com ele," "com ela," or "com você." In Continental Portuguese, however, "consigo" is a standard, natural, and frequent part of everyday speech when referring to the third person.

Brazilian Portuguese

In Brazil, "consigo" is used naturally in formal writing, journalism, or legal contexts.

1. O réu trouxe as provas consigo. (The defendant brought the evidence with him.)
2. O diretor não levou os documentos consigo. (The director did not take the documents with him.)
3. Ela sempre traz a sua determinação consigo. (She always brings her determination with her.)
4. O relatório traz novos dados consigo. (The report brings new data with it.)
5. O líder apresenta a sua visão consigo. (The leader presents his vision with him/as part of his presentation.)

Portuguese (Portugal)

In Portugal, "consigo" is used naturally in both spoken and written everyday language.

1. Ele trouxe as provas consigo. (He brought the evidence with him.) Note: A Portuguese person would naturally use the pronoun "ele" instead of the formal "o réu" in conversation.
2. Ele não levou os documentos consigo. (He did not take the documents with him.)
3. Ela traz sempre a determinação consigo. (She always brings determination with her.)
4. O relatório traz os dados consigo. (The report brings the data with it.)
5. Ele apresenta a visão consigo. (He presents the vision with him.)