Others have argued that there wouldn't be much difference. They might be right. Perhaps many of the changes were inevitable. However, I want to argue that there would have been a difference (perhaps just to be contrary). I'm going to assume that there never is a Black Death plague event, not just that it's delayed.
The Black Death made it easier to be a (surviving) serf. The shortage of labor meant that the aristocracy had to pay more attention to their serfs. Without that, there might never have been an English civil war. The anti-aristocracy movement might never have gotten off the ground because there wouldn't have been a middle class to fuel it.
Since the deaths were unevenly distributed (some families were wiped out while others were mostly intact), they had the effect of creating concentrations of wealth as some survivors were inheriting the wealth of many non-survivors. This created prosperity for some, allowing someone who had been poor to be at least middle class.
It's been argued that the aristocracy wouldn't have gone to the new world. But in a true feudal society, if the aristocracy didn't go, who would? Colonization was itself a result of the hungry middle class created by the Black Death.
Science and Engineering
Without a middle class, engineering would have been much weaker. Serfs wouldn't have been able to become engineers and aristocrats would not have wanted to do so. Science would be in a bit better shape, but there wouldn't have been as much science done by middle class engineering families (e.g. Huygens). There also wouldn't have been the same contributions from the judicial system (e.g. Descartes, Fermat, Pascal) as that would have continued to be controlled by the aristocracy.
Absent a middle class, we'd have failed to develop the Renaissance. Wealth would have been spread out more. Artists would have lacked the leisure to develop their craft and patrons would have lacked the wealth to sponsor them.
Without a middle class, Martin Luther would not have received the education that he did. Without that education, it seems unlikely that he would have become a friar much less the inspiration of the Reformation. As a serf, Martin Luther would likely be unknown to us today.
So given all that, we would be further behind in the sciences, have no serious engineers, a more monolithic religious regime, no colonies, and a system of serfdom. And we'd be stuck there, much as the Egyptians were stuck. Lacking barbarians to overthrow us, we'd stay in a feudal, dark ages system.
To reiterate, my basic argument is that the Black Death created the middle class by concentrating the wealth of certain families and by making labor more valuable. Since it was the middle class that drove many of the positive changes in the arts, science, engineering, religion, and exploration, those changes would not have happened. This would have left Europe in a more stagnant state.