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

No.

While the core meanings, spelling, and grammar of "empatar" are identical in both Brazilian and Continental Portuguese, there is a difference in typical usage. In Brazil, "empate" and "empatar" are frequently used in a casual sense to mean "to delay or hinder a person or a process" (e.g., "Não me empata"). In Portugal, while the word is the standard for sports ties, a speaker would much more naturally use "atrasar" or "impedir" when referring to delaying people or progress.

Brazilian Portuguese

1. O jogo terminou empatado em dois a zero. (The game ended tied at two-zero.)
2. Não tente empatar o meu trabalho. (Don't try to hinder my work.)
3. A seleção brasileira empatou com a Argentina. (The Brazilian national team tied with Argentina.)
4. Esse trânsito vai empatar a nossa saída. (This traffic is going to delay our departure.)
5. Eles conseguiram empatar a partida no último minuto. (They managed to tie the match in the last minute.)

Continental Portuguese

1. O jogo terminou empatado em dois a zero. (The game ended tied at two-zero.)
2. Não tente atrasar o meu trabalho. (Don't try to delay my work.)
3. A seleção empatou com a Argentina. (The national team tied with Argentina.)
4. Este trânsito vai atrasar a nossa saída. (This traffic is going to delay our departure.)
5. Eles conseguiram o empate no último minuto. (They managed to get the tie in the last minute.)