What fundamental causes are driving the asymmetry between US and euro-zone monetary policies?

We see that the Federal Reserve is now beginning the process of exiting its highly expansionary monetary policy, which is not at all the case for the ECB. This new asymmetry between the two central banks’ behaviour may have significant effects on capital flows and exchange rates. What is driving it? It stems mainly from the gap that has appeared between wage inflation rates in the United States and the euro zone, while in both cases “commodities” inflation will fall; And this gap between wage inflation rates stems from the gap between participation rates, the labour supply ha ving declined in the United States but not in the euro zone.