Sadly, not at the moment.
The inner workings of the Federation have been sketched out but they've never spent much time giving us any in-depth look at how well or badly the system functions. For instance, to what extent is corruption a problem? How about civil rights - to what extent is what we saw in DS9's Homefront/Paradise Lost indicative of larger problems? The jury is way out on both issues.
Since the Federation seems to have no huge problems the way the Republic does (civil war and degenerating into empire and whatnot), from the outside it looks like the Federation is a functioning system and the Republic is a disaster area. This may be unfair to the Republic because I'm watching
The Clone Wars which provides a far greater in-depth look into the political system, aka sausage making at its finest, than
Star Trek has ever bothered with.
the most significant difference between the two is that the Republic wasn't stupid enough to outlaw money, requiring it to become a Nanny state.
That's far from being the only significant difference, and presumably it only happened as of the 24th C, after the invention of the replicator, which changed the economy utterly. Money wasn't "outlawed," it just became irrelevant when everyone can get anything they want from a magic box.
Here's a far more relevant difference: the prequel movies and especially
The Clone Wars depicts the Republic as a squabbling, barely-hanging-together association of planets, maneuvering and trying to stab each other in the back, while the Federation has never been depicted as having internal disputes bad enough to fracture it entirely.
From the prequels, I got the impression that the Republic might just be the largely innocent victim of a machiavellian Sith conspiracy.
The Clone Wars provides much more damning detail, for instance, that the Separatists actually have some legitimate grievances with the Republic and aren't all just greedy capitalists and Sith dupes.
Also, the Republic countenances slavery (Clone troopers) which the Federation has never done. Imagine if the Federation decided that the Dominion was onto something, and they should start manufacturing their own Jem'hadar slave army. Then the Federation would be as bad as the Republic.
The Federation also relies for its defense on a meritocratic quasi-military organization, namely Starfleet, which anyone can join as long as they have sufficient motivation and drive. The Republic depends (stupidly) on a cabal of warrior monks who draw their membership from a creepy master race theory based on midichlorians. Furthermore, these warrior monks don't seem to be very good at their job, since they are incapable of seeing the huge threat in their midst. The Republic would be far better off if all Force-sensitive beings keeled over dead one day.
(Remember, I'm not talking about books - only TV and movies - in both cases. I don't have time to peruse every frakking
Star Wars and
Star Trek book in existence.)