Kor: "I have a great admiration for your Starfleet. A remarkable instrument. and I must confess to a certain admiration for you [Kirk] ... you of the Federation, you are much like us."
Kirk: "We're nothing like you. We're a democratic body."
Okay, it's not exactly clear in that case what Kirk meant by "we." On the surface he would appear to be referring to the federation itself, as the "democratic body." It certainly wouldn't have made any sense for Kirk to be referring to Starfleet by that term. So who then is the we? Humans only? Perhaps only those within the federation that Kirk felt personally akin to, but not the entirety of the federation.
I feel that if the federation is the diverse place that I see it to be (and want it to be), then the many worlds of the membership will have a wide variety of government types. However that doesn't preclude the membership's representatives to the federation council from using democratic procedures in council.
It's sort of funny that Picard never preached the virtues of a representative democracy...
When it comes to a particular government type, I can't remember Picard ever stating a preference.