I would say that the UN analogy holds well enough for what we've already seen on screen. Journey to Babel obviously established that each member world maintains its own diplomatic corps. But the analogy breaks down in certain areas. The UN for example does not maintain a unified armed forces of its own like the UFP does.
Personally I see the UFP as a more Federal type state, similar to the United States, Mexico, and Germany. It is one unified political body, but each member has a little more autonomy in certain areas than any state would in the US, Mexico, or Germany.
This.
But more specifically...I'd depict it as something similar to a USA-pre-Civil-War society--not with slavery, mind you, but when the 10th Amendment was more than a "truism"--with stricter state/planet sovereignty, where the UFP determines and regulates
interplanetary matters--such as the common defense and exploration. Individual rights are protected and defended, but matters such as commerce on planet are determined by
those governments.
This helps reconcile why some planets are depicted as trading with outside worlds, while the UFP as a whole is not.
I see the Federation as a place founded on promising, idealistic principles, but one that has come to value political expediency instead yet at the same time are in denial about the fact that sometimes tough measures have to be taken. They espouse diversity but are quick to lecture others. It's a weird combination, for sure--but that's what they have become.
I agree here, too.
Now...I strongly disagree with those who link the Federation to anything similar to Communism, or Socialism, or any other kind of Collectivism.
Perhaps it's an economic system different from anything we know of today--but it is certainly nothing involving centralized control over the economy, or over people's lives.
I personally liken it to a futuristic perfected free market economy, with a standard of living so high that the term "poverty" is effectively meaningless. Just as the poor of our society are quite rich in comparison to the poor of, say, Sudan (the majority of our "lower class" have TVs, cars, etc)--so those on the "lower rungs of the ladder" of the UFP would be richer than what we would call "middle class".
Nonetheless, the ladder still exists--for without a ladder, there is no progress.
Replicator technology, mass-produced, provides necessities so cheap it is as if money is unnecessary for those who desire nothing more than basic needs.
Still, pleasures would still be purchases--hence, credits, earned by work. Now...you think Joseph Sisko runs his restaurant while expecting nothing in return? Of course not. Money still exists in the 24th century--just in a different manner, in a way that Roddenberry couldn't explain.