Generally speaking, if you're planning to travel to and from the US, it will be easier to do with your US passport. As a non-US citizen travelling, you often get shunted to different, sometimes longer and more involved, lines in customs. Also, you're 'supposed' to use whichever passport of the country you're currently residing in.
However, if you wish to use your Icelandic passport, I don't think you'll have any trouble with that either - especially since politically, they're considered so harmless.
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My heart knows me better than I know myself, so I'm gonna let it do all the talkin'.
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