IMO, I think Russia would win. Or at least both sides will loose.
Air Force:
The number of US attack planes and fighters/interceptor aircraft is 4,872. All the aircraft involved in the Russian Air Force (trainers, transports, helis, attack planes, etc) is 3,082. 1,790 less planes than we have! So air force would be a win for us.
Link:
http://www.globalfirepower.com Navy:
The United States has 10 carriers. Russia has 1. We have 72 sub's. Russia has 63. Which most are soviet era sub's. We have 15 frigates. Russia has 4. We have 64 destroyers. Russia has 13. Russia, although has 74 corvettes. USA has none. Most ships in Russia's navy are soviet era. American ships are newer with better technology. USA would win the naval battle.
Army:
United States has 8,325 tanks (all are M1 Abrams). Russia has 15,500 tanks. Most are soviet era. America has 27,582 AFVs. Russia has 27,607.
Troops: Russia has more troops than USA.
The USA would win a conventional war with Russia. BUT Russia contains the most nuclear weapons. Russia has 369 ICBMs and 1,248 warheads. Russia also has 13 submarines with 591 warheads. Russia has 76 bombers with 884 bombs. The united States has 450 ICBMs, 113 bombers and 350 bombs, and 14 ballistic missile submarine 280 bombs.
Also, we have troops deployed in Europe that is close to Russia. We also have bases in Hawaii and Alaska. We would reach Russia easily.