We study the planetary nebulae NGC 7662 and NGC 7009 using a combination of imaging Fabry-Perot interferometry, narrowband filter imaging, and longslit spectrophotometry. This combination of techniques produces two-dimensional, flux-calibrated emission-line flux maps. The diagnostic emission lines He II λ4686, Hβ, [O III] λ5007, [N II] λ5755, [O I] λ6300, Hα, [N II] λ6584, and [S II] λλ6717,6731 are used to measure electron density and ionization state across the nebulae. The [S II] density maps show that the low-ionization microstructures (the [O I]-bright knots) are dense structures (except for the previously-identified FLIERS, as expected). The density maps also show that the observed bright-rim structure is dense, an observation that is in line with predictions of radiative-hydrodynamical models. Although the morphology, density structure, and ionization fronts in NGC 7662 and NGC 7009 all fit the predictions of the models, the central star observations of NGC 7662 and NGC 7009 indicate that these PNs are significantly older than the models they match most closely. In addition, the central stars of these two PNs have lower masses than the central stars assumed by the models. This contradiction is not easily resolved, and it may be premature to say that the models reproduce real PNs.