It's a too simplistic view about a complex situation.
Strictly about economic terms...
A simple answer: These circumstances certainly gives the edge to the country using FIAT currency.
Close to reality answer: Both countries will end up using FIAT and Bitcoin in order to take advantage of both currencies.
IMO, as soon we reach a moment where most of the countries starts adopting bitcoin, Governments as we know will fall. Most of people will simply skip taxes. That would mean large scale/long term wars will not exist anymore, it's simply too expansive.
Right, this is my point. It's too expensive for a country that's on a bitcoin standard. The countries that delay and use their money printer would be able to pay for wars for longer. Of course, I'd assume that eventually all countries would be forced to using a bitcoin standard, but until then, things could get messy.