Winter Euro-Atlantic atmospheric blocking events have significant socioeconomical impacts as they cause various types of weather extremes in a range of regions. According to current climate projections, fewer of these blocking events will occur as temperatures rise. However, the timing of such a reduction is currently highly uncertain. Meanwhile, recent studies indicate that using climate models with high enough ocean resolutions to simulate mesoscale eddies improve simulated winter Euro-Atlantic blocking events significantly. In this paper, we show from a large ensemble of climate simulations based on the highest emission scenario that largely prominent and coarsely resolved non-eddying climate models project a noticeable significant decline in blocking frequencies from the 2030s-2040s, whereas blocking statistics in eddy-permitting simulations are noticeably decreasing only from years 2060s. Our result suggests with a strong level of confidence that winter blocking activity over the next several decades will keep being dominated by internal variability.