Some blockchain projects claim to be more decentralized than BTC.
Do they succeed in this regard or do they face similar challenges?
Every challenge will never be the same, especially if the projects you are referring to have just developed in the current era where the momentum and environmental conditions themselves are also very different. Moreover, claims from one party like that will never be accurate so you yourself do not need to immediately believe their claims about being decentralized because so far I don't think anyone has been able to beat Bitcoin in anything including in terms of Blockchain development itself.
What lessons could BTC learn from these projects, if any?
If there are indeed and the innovation is truly new, of course it is not only Bitcoin who will learn the new thing, but there will be many other parties who will also see and analyze it so that it can be applied to their respective projects in the future. But I also want to know what project you are referring to because I don't see you mentioning the name of a project here.