The adsorption of a series of charged bottle-brush polymers with side chains of constant length on mica and silica surfaces is modeled using a lattice mean-field theory, and the predicted results are compared to corresponding experimental data. The bottle-brush polymers are modeled as being composed of two types of main-chain segments: charged segments and uncharged segments with an attached side chain. The composition variable X denotes the percentage of charged main-chain segments and ranges from X = 0 (uncharged bottle-brush polymer) to X = 100 (linear polyelectrolyte). The mica-like surface possesses a constant negative surface charge density and no non-electrostatic affinity for either the main chain or the side-chain, whereas the silica-like surface has a constant negative surface potential and a non-electrostatic affinity for the side chains of the bottle-brush polymers. The model is able to reproduce a number of experimental features characterizing the adsorption of the bottle-brush polymers for the full range of the composition variable X on the two surfaces, and thereby quantifying how the different nature of the two surfaces with respect to electrostatic properties and non-electrostatic affinity for the polymer affect the adsorption properties and the structure of the adsorbed layers. In particular, the surface excess displays a maximum at X ≈ 50 for the mica surface and at X ≈ 10 for the silica surface. Moreover, the thickest adsorbed layer is obtained at X = 10 - 25.