Neither country would fare well in trying to invade and conquer the other. Two many people, too much land, too much distance between them. The United States has dramatically superior force projection than the Russians at present. The U.S. Navy has 11 Carrier Strike Groups, the Russians don’t have anything that equals even one CSG, let alone 11 of them.
Depending on the geographic location of a conflict this could be a decisive advantage for the United States. For example any conflict outside of states immediately bordering Russia, Russia has to get there somehow. Imagine a conflict in say, Western Europe. The countries of Europe are almost definitely not going to give Russia free passage through their countries or passage through their air space. If Russia would even attempt to move significant forces through the Baltic or even Mediterranean they would be absolutely destroyed by the U.S. Navy. Aerial deployment would almost certainly be the preferred method.
What would be a significant deciding factor honestly would be where exactly this theoretical war would take place an the geopolitical situation.
For example if Russia invaded China they would have the advantage of proximity, they could bring the full force of their military to bear relatively quickly. Assuming the United States assisted China in defending itself, however, the United States has the support of the entire indigenous Chinese population and the full force of the Chinese military.
We’d see a similar situation repeated with all of Russia’s neighbors. Finland or Poland may not be as powerful as China, but they have powerful allies and the local population would resist Russian occupation. Russia would be fighting multiple enemies at once.
Now, if the United States was attempting to invade one of Russia’s neighbors, then Russia would have a clear advantage. They’d have proximity and the local population on their side. But honestly modern warfare being what it is, an invader is always going to have a very difficult time. Gone are the days in which the armies met in the field and then the defeated party sued for peace and made territorial concessions.
If we are to assume a contrived “neutral battlefield” (I say contrived because it’d be very difficult for a country to be neutral to two warring powers fighting on their land) then unless this neutral battlefield was one of Russia’s neighbors it would be very difficult for Russia logistically. We have much better logistics and force projection and would probably have tactical superiority from day one.
Geography would also come into play. In desert warfare the armor battle would be key as would control of the skies which is always crucial to any pitched battle in modern warfare. I think most neutrals observers will agree that the T-72 is inferior to the Abrams, and this has been proven in battle. Most Russian military supporters will point out to the lack of several key features that plagued the performance of Iraqi T-72s and argue that in any battle between the then USSR and the United States the Abrams would have been going up against superior tanks than what they saw in Iraq. That may very well be true, but from all that I’ve seen I think if you had to pick between being in an Abrams (all three variants) and the T-72 I’d prefer to be in an Abrams. The T-90 versus the most recent iteration of the Abrams is always a hot debate on internet forums but ultimately the T-90 has never really seen any service against modern armor; to me I just can’t really speculate about something that has never been in real combat. But American tank crews have a lot of combat experience and future tank crews have that combat experience which will be drawn upon in training. The fact that the United States has been involved in so many conflicts since the fall of the USSR has given it more experience across the board.
There are a whole series of debates that is opened up in the theoretical “open-field, full pitched battle in neutral territory” scenario. How does our Air Force fare against theirs? As just one example, and that in itself would be a multi-page debate.