"The Democratic People's Republic of fill-in-the-blank (Congo for example,)" appeals to all that is noblest and best in philosophies of Government.
Of the two, the Democracy of Athens is better understood than the Republic of Rome.
An Athenian could be part of a number of ecclesias, a Church a gang or a club, but entered upon (direct) Democracy only in the city gates. From recorded oratory of Socrates and Aristotle, sanity was not guaranteed... it was occasionally an oratocracy.
By contrast Plato's Republic represented all classes of society hierarchically, but not necessarily proportionately (or fairly?) To add to the confusion there was no written "Constitution," until 1786 for which the US may be justifiably proud.
Despite flaws and weaknesses, historically the tortured wheels of justice turned farther in Republics than Democracies, Kingdoms or Communes. Look no farther than Socrates' trial.
A glance at Latin Proverbs of Philosophy and Government will show that Italian Latins left many warnings behind as their civilization fell, trade ships leaving Rome empty without exception.
Here is
a list, I recommend Plato, Cicero, Horace and even Juvenal.
Positive law is not addressed directly by Democracy; In a Republic the highest of the high is "under law." Positive law depends on manipulation and subversion of choice by a benevolent tyrant, and fails upon his death - see 'The education of Cyrus,' by Xenophon.
From these historic foundations I have always chosen the GOP to defend the constitution against all enemies, both foreign and domestic. These are embarrassing times to be Republican. The party has strayed. It needs to return to the fundamentals of Republic; America under God and under law, with liberty and justice for all.