EretzHaK, see Rav Bleich’s article ‘Capital Punishment in Noahide Law” in “contemporary Halachic Problems” vo. 2. There he discusses the issue of the jurisdiction of non-Jewish governments over Jews in criminal cases. In any event, according to Rav Schachter a democracy is a partnership between all citizens, Jews and gentiles so it would seem that all would agree that it has the power of mishpat hamelech. Please cite sources for the greater severity of punishment in harming a Jew (and note the Meiri’s well-known exception). In an ycase, according to Rav Schachter one who steals from a democratic government also steals from Jews. The should be obvious as all taxpayers are harmed.
As for the appropriate punishment, it depends on the crime. Someone who evades $1,000 in taxes should be fined although he probably is not worth the trouble and expense of trying him. For someone like Madoff or Shalom Weiss who ruined people’s lives a symbolic death penalty such as they received is totally appropriate.
The place of the battei din in all of this is educational due to the enormous chillulie Hashem created. In fact, various rabbanim in conjunction with figure such as Benjamin Branfman has been conducting yamei iyun on this subject.