If it was a conventional war, and it happened today, not taking into account American forces are spread out in the Middle-east.
One really would just need to look at how well Iraq did in the Gulf and present war, armed with Soviet weaponry. The conventional war lasted mere days, and the Iraqi Army and Air Force were in shambles. There were very casualties sustained by the US during the conventional war.
However a lot of this was due to very clever diversions and stopping 200 Russian Kornet anti-tank weapons from entering the country. One could only speculate if the Soviets would fall for any of these ruses, and certainly they would have their anti-tank busters on hand. (A Kornet is the only weapon that can take out an Abrams.)
Their tanks are no match for an Abrams, and they lacked communications equipment. We would also have to take into account on which continent this pretend war would take place. Either side would have difficulty fielding enough logistically to fight a war. I think logistically the Americans would have the advantage in being able to quickly deploy troops, tanks and fighters to launch an invasion.
If the war happened in Russia I think the US would still have the advantage, because the Soviets were so interested in disinformation they printed false maps and the only ones using these maps were the Soviet Generals. Tank commanders regularly got lost on exercises. The US had updated imagery on a daily basis and made their own maps. Hopefully we wouldn't make the same mistakes Hitler and Napolean did in fighting on their turf in the winter.
After losing several battles, the Soviets in desperation would still launch their nukes and all would be lost anyway.