Not necessarily; we don't exactly skimp on the war-chests. Higher infrastructure could just as easily mean nations are spending money on infrastructure more freely rather than saving it.
Honestly, the outcome would depend on the definition of "winning" you use. If winning means causing more damage to the opponent than one receives in a set period of time, I would bet on us, by virtue of having a more developed top-end, a slight nuclear superiority in the middle-lower ranges, and having a higher tech-to-infra ratio. (In war, infrastructure is far more perishable than technology.)
If, on th