China isn't exactly claiming to "catch up" with US in many aspects, say in economic structure, taxation, weight of defense in national economy (DoD alone takes 4.5~5% of GDP, excluding other defense related branches), demographics (immigrant country), weight of virtual economy (US controls the international reserve currency), social welfare net, etc.
Instead, Mainland China's ultimate goals include full-scale industrialization, balance between market-driven commodity economy & state-driven social welfare (& infrastructure, i.e. balance between free market & socialism), low defense spend, homogeneous & cohesive demographics, and a favorable international trade structure, etc.
Therefore socio-economic models of some advanced economies in East Asia (including independent economies of Greater China) are better references, making more pragmatic benchmarks.