First, there are two kinds of resolving power, angular, and linear.
Angular resolving power is primarily a function of aperture and is relatively unaffected by optical power or things like a secondary obstruction. In other words, the larger the aperture, for given wavelengths of light, the smaller the Airy Disk of a star will be, and this is what the formulas you have been given will show you. Again, this figure is for angular resolution and is typically based on the telescopes ability to separate double stars. Because the Airy Disk of the double star grows smaller with aperture, the larger the aperture, the more space there will be between the stars.
For extended subjects like planets, and the low contrast detail on their surface, linear resolving power and more importantly, contrast transfer function, describe how "Sharp" the view in a given telescope will appear. Optical engineers use linear resolution or encircled energy to describe how much contrast the telescope will loose due to the aperture, the presence of a secondary obstruction, chromatism (color error), and optical quality. This means you can have a smaller telescope with more perfect optics, smaller (or no) obstruction, no chromatism (rare) and perfect optics, and it could make very low contrast detail like faint festoons on Jupiter's surface easier to see in a smaller telescope than in a larger telescopes. This is not always true and generally the larger telescope starts with better contrast transfer, but better contrast transfer is what allow you your eye to resolve low contrast detail on extended targets.
So, even poor telescopes can resolve equal brightness double stars as well as the formula predicts (better sometimes in fact because some errors make the Airy disk appear smaller) but for planets, the best telescope to resolve low contrast detail will be the one with the best contrast transfer and that is not always going to be the larger telescope.