I imagine that day-to-day life in the Terran Empire for most people is akin to day-to-day life in the Third Reich, in Franco's Spain, Chile under Pinochet, or Argentina under the military junta. It does seem to be a totalitarian state; it doesn't seem to have any egalitarian rhetoric, implying that it's not what we would call a "nominally leftist" dictatorship.
The MU always struck me as more piratical than totalitarian in the sense we're used to, the notion of some government with total control over people. In TOS especially, the structure seemed a lot looser and more chaotic, with people being encouraged to commit murder in order to advance.
Really, it doesn't seem like a society that could exist on an ongoing basis, but assuming it could, it's more like libertarianism or anarchy run amok than fascism or communism. Or even the ultimate in laissez-faire capitalism, with the entrepreneurial spirit encouraged to a murderous degree.
In other words, if Americans invented a totalitarian system, it would be the MU.