The fact that we ouspend them several times over mean that the funding isn't the problem, not that we'd win. Without an unified army, we're at a big disadvantage, and I don't know how ready we are for a conventional war. Could we even supply our troops with enough ammunistions? I recall that it became a problem in Lybia.
How are we at a big disadvantage? Europe forms coalitions at the bat of an eyelid and has been doing so for a hell of a long time. Even got historic precedents for it. Logistics wasn't an issue, no one was running out of ammunition except maybe rebel sleeper cells. The issue was public support, this was one of the first military interventions where the US populace who were sick of military intervention were finally reaching majority. Between Britain and France you already have 400,000 of the best soldiers in the world with both nations heavily invested in power projection. Its intelligence services are world class, navies are world class, air forces are world class, its special forces are used as models for the rest of the world's special forces all over, its fleet auxiliary is superb and its soldiers are the veterans of many recent wars.
Russia's military is formidable but I never trust in the strength of an army if the majority are conscripts.
Though I suppose one thing to factor in is that Western Europe's relationship with their army is complicated. Russian pride in power is ostensible enough but Western Europeans tend to be caught between shame and indifference with their armed forces, wishing to cut it down to a smaller reservist force, or pride and support, wishing to increase the defence budget and its active force. It's in a vary precarious position.