Since this is a hypothetical war, and you didn't say who was invading who [even though we all know who it would be] we'll assume that the war will take place at an equidistant, neutral location; so transportation costs are at an equal level. We'll also have to take alliances out of the equation since this is purely Country v. Country.
In such a case, USA would win, because the United States has the upper-hand in nearly everything else.
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