Limitations of extremes for the exchange-correlation functional - DFT
One way to begin to gain some insight in this is to consider the work done on benchmarking density functionals. I shamelessly plug the work done by my old group, which can be found here. The GMTKN30 data include results for Hartree-Fock and LDA functionals with large basis sets. The description of the several benchmark sets involved and the analysis in the actual paper will illustrate many of the shortcomings and strengths of these approaches (and why better, more pragmatical DFT approaches are more widely used). While I have no access to the GMTKN55 paper, I trust that it contains references to other benchmark papers that may actually deal with crystals.