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You are correct, the computation is quite complex.
But assuming that the bulk of the family income is earned by an American (OP did not state her husband's nationality) and taking the convoluted US tax code and double taxation treaties into consideration, the bottom line is that one's total tax liability is usually fairly close to what one would have owed to the US if one were US resident.*
Living in a low tax canton means less credit for foreign taxes paid, and one ends up paying a chunk to Uncle Sam that would have gone to Helvetia if one lived in a higher tax canton. Now that opens a whole different can o' philosophical worms, though...
* Either that, or I need a new accountant.
ETA: There are indeed advantages to living in a low tax canton for Americans, as tax planning can be simpler. Plus one doesn't feel the bite of the AMT as much... There may well be advantages I don't know about, as my eyes tend to glaze over every time I try to read an IRS document...
ETA II - Good point about being retired; I really don't know how the US/CH tax issues affect non-earned income. I don't plan to worry about that for a few years yet.