I am not an expert in Hegel or Ibn Khaldun, but I'm not sure that they're making the same point. I don't think Ibn Khaldun means that this process leads to progress; it's just a description of changes over time. The new civilization isn't necessarily superior or somehow more developed than the previous one.
Hegel, on the other hand, is very much wrapped up in the "progress" concept:
Hegel’s dialectical method leads to concepts or forms that are increasingly comprehensive and universal. As Hegel puts it, the result of the dialectical process, "is a new concept but one higher and richer than the preceding—richer because it negates or opposes the preceding and therefore contains it, and it contains even more than that, for it is the unity of itself and its opposite."
