To investigate whether distinctions exist between low and high-luminosity Class II 6.7-GHz methanol masers, we have undertaken multi-line mapping observations of various molecular lines, including the NH3(1,1), (2,2), (3,3), (4,4) and 12CO(1-0) transitions, towards a sample of 9 low-luminosity 6.7-GHz masers, and 12CO (1-0) observations towards a sample of 8 high-luminosity 6.7-GHz masers, for which we already had NH3 spectral line data. Emission in the NH3 (1,1), (2,2) and (3,3) transitions was detected in 8 out of 9 low-luminosity maser sources, in which 14 cores were identified. We derive densities, column densities, temperatures, core sizes and masses of both low and high-luminosity maser regions. Comparative analysis of the physical quantities reveals marked distinctions between the low-luminosity and high-luminosity groups: in general, cores associated with high-luminosity 6.7-GHz masers are larger and more massive than those traced by low-luminosity 6.7-GHz masers; regions traced by the high-luminosity masers have larger column densities but lower densities than those of the low-luminosity maser regions. Further, strong correlations between 6.7-GHz maser luminosity and NH3(1,1) and (2,2) line widths are found, indicating that internal motions in high-luminosity maser regions are more energetic than those in low-luminosity maser regions. A 12CO (1-0) outflow analysis also shows distinctions in that outflows associated with high-luminosity masers have wider line wings and larger sizes than those associated with low-luminosity masers.