Using the object with C \setminus b is equivalent to U \setminus L \setminus b, not to just L \setminus b. That being said, there is an issue (hopefully to be resolved soon) where the Cholesky-object ldiv! is currently slower than it needs to be — see Ldiv for Cholesky is slower than two substitutions - #6 by danielwe and Triangular solve and inversions have poor performance · Issue #1405 · JuliaLang/LinearAlgebra.jl · GitHub
PS. I would generally wrap C.U in an UpperTriangular object to make sure that Julia exploits its structure, although in practice ldiv! checks for this.