Hmm. Interesting question, particularly in a modern sense. The outcome of protracted conventional wars seem to be affected as much by the availability of materials and infrastructure as it is by leadership skills or technical edge, so there's many factors to consider. In the area of manufacture NATO has a clear advantage, since without nuclear weapons Russia would have a hard time permanently affecting the manufacturing capability of North America, whereas Russian manufacturing capabilities could be limited to those production facilities east of the Urals due to NATO bombing campaigns. Terrain in general favors Russia, particularly in winter, but overall technical superiority goes to NATO, which boasts everything from more accurate standard issue rifles (the AK12 has not yet been fully issued to all Russian Ground Forces troops) to more sophisticated drone and satellite systems. Russia does have a technical edge in fighter technology and may even have a more advanced main battle tank than anything NATO currently fields, but in a combined arms scenario the SU35 and T-14 would not likely be enough on their own to gain battlefield superiority. In terms of leadership capabilities NATO maintains a slight advantage over Russia, with more widespread recent combat experience in the Middle East and Africa than Russia in Syria and Crimea. However in terms of current leaders, President Vladimir Putin has demonstrated himself to be a much more competent, cunning and capable leader than the American President Donald Trump, and even though both leaders would likely listen to the opinions of military minds, Trump's stubbornness and possible instability have to be taken into account when considering a war that would likely last years and take a toll on every facet of life. The European Union does have more stable leadership under Donald Tusk, Jean-Claude Juncker, Antonio Tajani, Angela Merkel and Emmanuel Macron, however EU leadership has suffered damage to its authority with the announced departure of Great Britain and the United States' shifting allegiances from Europe towards China. With all this in mind it is hard to say if there would be a clear victor. With North American assistance to Europe, technical superiority and more reliable manufacturing, it is likely that NATO would win in name, however with Russia's terrain advantage, numerical advantage and detestment of the possibility of a European invasion, it is likely that Russia's military would permanently damage much of the European continent, rendering any long term NATO victory Pyrrhic. This Pyrrhic victory combined with less than ideal leadership throughout NATO would not bode well for its members in the long term, whereas Russia could likely recover from all out war more efficiently due to its more stable leadership.
TL;DR - if trump wasn't president of the united states maybe nato would win, but imo a modern day warsaw pact would win in the end