Proponents of one system over the other worry that voters will get confused, or worse, that established groups that disagree with the reform could attack a new voting system as too complicated.
Personally I think this is part of the reason approval has gotten more traction than score or STAR systems, but who's to say. The Center for Election Science has better PR and web design than https://www.rangevoting.org/, which largely advocates for Score voting.
But it's a multifaceted issue. Academics argue over different methods, and even as a casual observer it seems pretty clear that no system is flawless.
For anyone who hasn't read "Gaming the Vote" by Poundstone, it's a useful introduction that discusses both the academic study and practical use of voting systems.