The issues are much trickier than a debate of "which state is more oppressive?" would suggest. Clearly (as the movement of individuals from totalitarian to democratic states would suggest) capitalist democracies like the US do not rely so much on direct, brutal force (although they still rely on it to some degree, of course) and so for most citizens the perception is that such societies are more "free". On those grounds the cold war is over, the debate has been won, the US is the spiritual world leader it imagines itself to be, etc., etc.
However, I agree with JHatman that we are suckers if we buy into the "terrorism" language that invites us to imagine that other people do things for inexplicable "evil" reasons, and discourages us from trying to understand the genuine reasons that motivate all political activity, however bizarre it may seem from "the other side". I agree that just as yesterday's "terrorists" are today's "freedom fighters" or whatever, it's entirely possible that Muslim extremists may one day be written about as some of the last, desperate resistance against the incredibly powerful and persuasive system of political control that we call "democracy".
An important key to understanding the power of capitalist democracy as a system of political control is the phrase, "the manufacture of consent". Capitalist democracies do not rely so much on overt force (the violence of batons and torture and so on) because they rely on PRODUCING the desire to conform and obey in citizens. Every child in a Western democracy is bombarded from infancy with stuff that we think of as "normal life" but other forms of society would regard as "propaganda": everything from parents' toy choices to the educational curriculum to the endless TV advertising to the popular music and so on and so on, all work to produce adults who WANT to spend their entire lives working to generate profits for their economic superiors. In other societies a slave knows s/he is a slave, because the desire is to escape from the work. In capitalist democracies, a slave imagines s/he is "free" because s/he "chooses" to pursue the big-screen TV's and other crap that signifies "the good life" in a consumerist society: it is basically a case of cleverly replacing sticks with carrots until the slaves are mostly content. When they object (as the poorer parts of society in capitalist democracies tend to do, e.g. black Americans) then the sticks come out (e.g. prison).
This is still a vast over-simplification, but the point is that we are used to thinking in terms of "my free, independent choices are either constrained by violence, or they're not", which clearly points to the US as vastly superior to a religious Islamic state. However, there is a sense in which the most extreme form of violence is to mess with the "free will" itself; to groom citizens into creatures who desire nothing more than to stuff their living rooms with plastic toys and fantasize about better sex or idealized romantic relationships, so that the genuinely social "political" activities that are part of real, fully human living fade into the background and cease to be important. Who is the more seriously abused: the child who hates and fears his abusive parent, or the child who loves to be sodomized by the parent who has carefully raised the child to desire abuse? When you look at it in those terms, which is the worse society: the "totalitarian" society where the citizens are aware of the state's imposition into every aspect of their lives...or the capitalist "democracy" where the citizens experience themselves as being "free", even as they get up every day to perform meaningless work for the benefit of wealthy elites, just as their medieval ancestors did?
In the end, the issue of distress (how "unhappy" citizens are about their political superiors) is only one issue among many. The character of "Reagan" in the film "The Matrix" is a nice metaphor for this thing of happiness versus freedom: he discovered that genuine freedom was frightening and uncomfortable (because it involved AWARENESS of state violence and the poverty of real human freedoms), so asked to become a slave again in order to feel happy. In fact the whole idea of "The Matrix" is a pretty good metaphor for capitalist democracy: a citizen's life energy is exploited not because the citizen fears the state's violence and power; but because the state has so effectively imposed itself upon the citizen's perceptions and desires that the citizen is not even free to experience the lack of freedom. As every advertising professional knows, desire itself can be produced and manipulated, and capitalism paired with democracy is the perfect union of unrestrained power-seeking (capitalism) with a politics of popular desire (democracy), allowing the powerful to become endlessly more so, simply by directing their power at public perception.
This is not to say that our democratic freedoms don't count: I greatly appreciate the fact that I can post what I am posting now, whereas in a totalitarian state, if I pointed out that elders were manufacturing the desire to worship Allah (or whatever) in children then I could have my tongue chopped out or teeth kicked in or whatever. All I am saying is that there are pros and cons and that JHatman is right to question the simplistic "we good, they bad" explanations with which people like to comfort themselves. Perhaps my tongue's being chopped out in a totalitarian state is evidence of my tongue's power to incite real change and significant "freedom" in a society that knows itself to be oppressed, whereas in a capitalist democracy, there is simply no need to chop out my tongue, because it has no power to do anything in a population that is socially/politically/spiritually asleep.