Vortex disordering in superconducting crystals is shown to be markedly sensitive to penetration-depth anisotropy. At low temperature and high magnetic field, the muon-spin-rotation spectra for the highly anisotropic Bi[sub 2]Sr[sub 2]CaCu[sub 2]O[sub 8+[delta]] material are found to be anomalously narrow and symmetric about the applied field, in a manner consistent with a layered vortex sublattice structure with pinning-induced misalignment between layers. In contrast, spectra for the less-anisotropic YBa[sub 2]Cu[sub 3]O[sub 7[minus][delta]] compounds taken at comparable fields are broader and asymmetric, showing that the vortex lattices are aligned parallel to the applied-field direction.