Dual passports is usually a win.
Not only are there some countries that won't like one or the other of your kids citizenships (solution: travel there on the other passport), some countries will give you a really hard time if you try to go there, but have a stamp from another country they don't like.
In addition, if you have a stamp from some countries, other countries won't let you work there. For example, it used to be that if you had an Israeli stamp in your passport, you were barred from Egyptian archeology.
Note that your kids need to do this before they are 18; after 18, they can be required to renounce U.S. citizenship to obtain alternate citizenship, and vice versa; a lot of children of Irish immigrants to the U.S. have found this out the hard way, for example, when they decided after age 18 to claim their Irish heritage, and use that to take advantage of opportunities to study in Europe, rather than going to a U.S. university.
Finally, they can always renounce later, if they become Internet billionaires, like Eduardo Saverin, who the U.S. effectively paid $700M to renounce his citizenship, although there's a 15% "exit tax", so if they go this route, they should do it *before*, rather than *after* the IPO - he'd have been another ~$300M richer if he'd done that and left the country before the actual IPO.