Experimental developments in neutrino telescopes are drastically improving their ability to constrain the annihilation cross-section of dark matter. Focusing on particle models for dark matter, we assess how these future limits will complement the existing landscape of dark matter searches. We bring together results from gamma-ray telescopes, measurements of the cosmic microwave background and direct dark matter detection. Our projections are based on the Angular Power Spectrum method, which is a powerful tool for reducing astrophysical uncertainties. We find that neutrino telescopes will be able to competitively probe significant portions of parameter space and will provide critical complementary information to the search for dark matter. Furthermore, we identify models that can potentially be explored where the relic abundance is achieved through thermal freeze-out.