Can we assume that things have always been this way? So all the brainpower and money that was spent designing and researching weaponry was spent optimizing weaponless combat since the beginning of warfare? I imagine the emphasis would then be placed on training, physical enhancement, military intelligence, and deployment speed.
It would still end up being whoever spent the most money who had the best army. We'd have been genetically enhancing our soldiers about as soon as that was feasible. Since necessity often dictates morality, no one would have a problem with it in this alternate universe. Soldiers who were stronger and more resistant to high g-forces could be loaded into supersonic jets that were designed to perform far beyond what a normal human could tolerate and deployed in the battlefield almost as fast as we realized we needed reinforcements.
Satellite technology would be important for intelligence, so we'd be far more advanced in that area than we are currently, the same would be true for drone technology. Mobility would be key. Getting more forces to strategic locations is probably the most important factor in warfare. Faster and planes, jets, cars, trucks, and boats that are capable of carrying greater numbers of troops are all areas that would turn the tide in any war.
There would be more emphasis on strategy. Strategic withdrawals, advances, feints, and dodges would need to be carefully orchestrated to catch enemy armies in situations where they are at a numerical disadvantage without being able to reinforce. Once again that goes back to whoever has the superior intelligence. Satellites, drones, spies, double agents, prisoner interrogation and torture, along with other covert operations would be more important than ever.
Who would be able to throw themselves into the research of all this?
My vote: 'Murica