I would say read the policies VERY, VERY carefully. Especially the expat policy. You need to make sure you understand both what it covers and how it pays. Know that the international standard for medical care is cash on the barrel, and that hospitals will very often look at your wallet before they look at your injury, so in a lot of situations you may be paying and waiting for reimbursement.
So first, what does your international policy cover? Routine health care? Pre-existing conditions? Medications? Who is making the decision about what is covered, and how do they do that -- if you end up with some treatment that is the standard of care where you are, but wouldn't be done in an American or European hospital, will they pay for it? Whose responsibility is it to translate claims, yours or theirs? How do you get medication -- can you access US pharmacies through mail order? How do you get paid; in what currency and at what exchange rate? Does your policy cover medical evacuation -- and if so, to where? If they medevac you to the US (or your home country), does the international policy still pay? If not, you want to be VERY clear about under what circumstances you'd be medevaced and how that decision is made, and may want to carry a US Policy as well. You also want to be clear about what forms of Medical Evacuation are covered (life-flight? commercial air? with or without an escort? who pays for that?) and whether there are specific companies you need to work with and what their coverage areas are.
Understand that often commercial carriers in other countries are very, very strict with what conditions they allow people to fly under and may require medical documentation or a medical escort for things we consider to be mundane. Further, medical evacuation -- which can be necessary for all sorts of sudden-onset conditions, illnesses and injuries -- is enormously expensive. We used to have to fly people 150-200 miles to Miami and it would run $12,000 to $15,000 -- again, cash on the barrel. So that's some context to solve against when you're thinking about the kinds of fees you'd insure for.