The two movements are distinct, with differing geneses, differing tactics, differing goals, and markedly differing positions on the West.
Where Shia Islamism is concerned, clandestine "meddling" is the centerpiece of their relationship with the United States and other western powers. They don't seem as concerned with Western cultural norms. While it is true the Iranian government prohibits alcohol and has codified in law standards of dress for women, their government is at least ostensibly a republic (a Greek tradition) and the Iranian people are voracious consumers of Western cultural exports. Above all, however Shia Islamists have shown themselves far more capable than Sunni Islamists of drawing distinctions between Western government and westerners more generally. You could travel to Iran without much worry of being kidnapped and/or butchered (but you could be mistaken for a CIA agent and thrown into Evan prison).
So yes, American interventionism is a much bigger issue for Shia Islamists than for Sunni Islamists, while the clash of cultures plays a rather diminished role.
But I don't think Shia Islamism is as big a problem as Sunni Islamism. Yes, civil rights conditions in Iran are deplorable by any objective measure, but civil rights in, say, Saudi Arabia are much worse. It may be in part due to Persia's illustrious past, and strong historical connection to Europe, but the Iranian brand of Islamism is much more subdued in its fanaticism. Women are certainly constrained, but they are educated, and many hold high-ranking positions in the secular government. Also, while they will never admit to it openly, the Iranian government is known to work with western governments when it is in their interest to do so (Iranian support was crucial in our initial expulsion of the Taliban from Afghanistan). Lastly, while it may be mostly lip service, Iranian politicians speak a good deal about peace and international cooperation, regardless of religion... which is something you'll never catch ISIS or Al Qaeda doing.
At the very least, the Shia Islamists seem content to mind their own business. The only outlier, it would seem, is Hezbollah, which even then is more Israel's problem than ours.
It is good the Middle East didn't go the way of Japan, but given the cultural traditions of each respective region, that's not surprising. For centuries, the Japanese have valued order, conformity, loyalty, and martial prowess. The idea of nation/states is something a novelty to the Middle East; theirs was, and in some ways is, a tribal society. "Arabism" didn't become much of a thing until the end of World War I.
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