We consider a model fluid with long-ranged, dispersion interparticle potentials confined between competing parallel walls. One wall is solvophilic and would be completely wet at bulk liquid-gas coexistence while the other is solvophobic and would be completely dry at bulk coexistence. When the wall separation L is large and the system is below the bulk critical temperature and close to bulk liquid-gas coexistence, a `delocalized interface' or `soft mode' phase forms with a liquid-gas interface near to the centre of the slit; this interacts with the walls via the power-law tails of the interparticle potentials. We use a coarse-grained effective Hamiltonian approach to derive explicit scaling expressions for the Gibbs adsorption, the surface tension, the solvation force and the total susceptibility. Using a non-local density functional theory (DFT) we calculate density profiles for the asymmetrically confined fluid at different chemical potentials and, for sufficiently large L, confirm the scaling predictions for the four thermodynamic quantities. Since the upper critical dimension for complete wetting with power-law potentials is <3 we argue that our (mean-field) scaling predictions should remain valid in treatments that incorporate the effects of interfacial fluctuations. As the wall separation L is decreased at bulk liquid-gas coexistence we predict a capillary evaporation transition from the `delocalized interface' phase to a dilute gas state with just a thin adsorbed film of liquid-like density next to the solvophilic wall. This transition is connected closely to the first order pre-wetting transition which occurs at the solvophilic wall in the semi-infinite system. We compare the phase diagram for the competing walls system with the phase diagrams for the fluid confined between identical solvophilic and identical solvophobic walls.