Matter effects contributing in solar, atmospheric and reactor neutrino oscillations Neutrino oscillations are affected by the matter effects. For solar neutrinos, which are exclusively neutrinos of $\nu_e$ type, the matter effects can be contributed by (i) the solar plasma, (ii) atmosphere and lastly (iii) the earth's core before they are detected by underground neutrino detectors. Which one of these sources of matter effect contribute the most and why? What about atmospheric and reactor neutrinos?
 A: The short answer: definitely the Sun!
The reason you may not have found a definitive "the sun is more important" in your search is that the effects of the Earth's interior are so insignificant compared to the Sun's interior that most authors wouldn't even bother to point this out. In fact, the effect of the Earth's interior are so small that until a few years ago it was hard to even detect them. Whereas the effects of the Sun's interior have been measured and known at least since the 80's, possibly sooner.
To expand on this a bit, the reason neutrino oscillations are affected by matter is due to scattering of neutrinos through electronic interactions. See this paper (which also incidentally contains a lot of calculations for the oscillation in both the Sun's interior and the Earth's interior). Thus they are pretty much entirely dependent on electron density, and the electron density of the Sun's interior is about 10x that of the Earth's interior, furthermore the Sun is about 2 orders of magnitude larger in diameter than the Earth.
The strength of matter effects also depends on neutrino energy; higher-energy neutrinos are more affected. The effect was first characterized in 8 - 18 MeV neutrinos; neutrinos under 2 MeV don't seem to be affected, see this paper.
All of this said, we don't have an ideal 'matter-free' beam of solar neutrinos to compare against, so all of these results are based on computations from models.
As for atmospheric neutrinos, the same kind of reasoning applies: the Earth's interior would cause much larger oscillation effects than the atmosphere, assuming the neutrinos pass through any significant chunk of Earth.
