There is growing observational evidence that disk evolution is stellar-mass dependent. Here, we show that these dependencies extend to the atomic and molecular content of disk atmospheres. We analyze a unique dataset of high-resolution Spitzer/IRS spectra from 8 very low-mass star and brown dwarf disks. We report the first detections of Ne+, H2, CO2, and tentative detections of H2O toward these faint and low-mass disks. Two of our [NeII] 12.81 micron emission lines likely trace the hot (>5,000 K) disk surface irradiated by X-ray photons from the central stellar/sub-stellar object. The H2 S(2) and S(1) fluxes are consistent with arising below the fully or partially ionized surface traced by the [NeII] emission, in gas at about 600 K. We confirm the higher C2H2/HCN flux and column density ratio in brown dwarf disks previously noted from low-resolution IRS spectra. Our high-resolution spectra also show that the HCN/H2O fluxes of brown dwarf disks are on average higher than those of T Tauri disks. Our LTE modeling hints that this difference extends to column density ratios if H2O lines trace warm > 600 K disk gas. These trends suggest that the inner regions of brown dwarf disks have a lower O/C ratio than those of T Tauri disks which may result from a more efficient formation of non-migrating icy planetesimals. A O/C=1, as inferred from our analysis, would have profound implications on the bulk composition of rocky planets that can form around very low-mass stars and brown dwarfs. ; Comment: Accepted to ApJ