I am curious how such a hypothetical confrontation could look like. In an all-out war with NATO I don't see how Russia would be able to put up a real fight. Then again, I was sure Ukraine would fold in a week. And here we are.
I'm going to answer that here since it seems more appropriate. I think that a confrontation like this would likely escalate from something smaller, perhaps an attempt to shut down Russian sea traffic through the Baltic or blockade Kaliningrad, or start downing Russia inbounds over western Ukraine, possibly under the theory that they're about to cross into Polish or Romanian airspace. It would be something of that sort that Russia responds to forcefully, and the situation escalates from there. It would require in principle some EU actors to feel confident enough in their military capabilities to stand up to Russia which I think is still some time away. So the start point wouldn't be a EU/NATO buildup for the war, but some lesser situation escalating.
As to whether Russia would be able to put up a real fight, it really depends. Again I don't think we're talking about a large EU or NATO ground force. We're probably talking about a war in the air and on the sea. The latter Russia would lose and badly, almost certainly. But the former isn't quite so obvious. Russia's IADS is very large, and has learned some lessons from the current war. Russia also continues to produce modern SAMs in large quantities. So if Russia's jets mostly stay well back and trade potshots, like they do over Ukraine then EU/NATO legacy jets would have a hard time penetrating Russia's IADS. Europe does have a small quantity of F-35s but considering geography and where they operate out of, and op-tempo, they couldn't be the sole combat jet that gets used. Throw in the possible use of air-air tactical nukes, and Russia's robust strike arsenal being able to reach many of the bases EU/NATO would be relying on (allowing them to disrupt operations there and possibly even hit jets on the ground), and the air war is not so simple to predict the outcome of.
Consider what Iran was able to do to US military facilities across the Middle East and what impact this has had on US operations against Iran. Certainly I think Russia would put up a real fight. I do think it's a fight that would very likely head towards tactical nuclear weapon use quite rapidly. In theory EU/NATO can respond in kind, in practice the arsenals are not comparable unless the US gets involved. In a theoretical medium term where the fighting somehow doesn't turn nuclear, Russia would almost certainly lose. But in a significantly shorter engagement Russia could theoretically do enough damage to EU/NATO bases and facilities to disrupt air operations, and largely hold their own in the sky, losing some SAMs and planes but not losing their actual IADS.
It the EU/NATO forces do want to send large ground forces in that would change the calculus considerably. They could almost certainly overrun Kaliningrad, and hope that doesn't trigger a nuclear response. It might not. But then what? Are they also at war with Belarus? If no, it makes for some awkward geography. If yes, the fight would be in Belarus. Russia would have a fairly easy time rushing troops to Belarus, and would have the Belorussian military as allies. There already are Russian nukes in Belarus and the IADS is already integrated. And while Belorussians don't necessarily like Lukashenko, their reaction to a foreign military force might not be friendly, especially if the invasion comes with heavy fighting and large scale destruction. It's an open question as to just how well EU/NATO forces are prepared for the modern drone-infested battlefield, but I suspect they're worse prepared then Russia is. Russia's military lives there. It's not a fight that would be easy or have a simple obviously predictable short term outcome for either side in my opinion. Again in the medium term, if the war somehow doesn't go nuclear and lasts that long, it would eventually go badly for Russia. How badly and how quickly is an open question.