Who on earth would be " a conservative version of Souter." Wouldn't such a person have to appointed as a Liberal by a Democrat and turn out to be a Conservative. Come to think of it, I don't think that has ever happened to the Liberals; when they appoint a Liberal, they get a Liberal. It is only the Conservatives that appoint a Conservative and get a Liberal.
I think you're right. Leftist Democrats are astoundingly good at getting what they want on the bench: statist, anti-gun, anti-traditional family, pro-choice judges.
Republicans are absolutely terrible at it, and have an awful track record.
What is the difference? Leftist Democrats are very comfortable with the secular humanist ideology of their base, and Republicans are deeply uncomfortable with the ideology of their base - religious conservatives, economic conservatives, combination, etc.