From what I know, V-Ray is the most realistic render engine out there. But, I also know that Cycles is physically accurate. How is Cycles different from V-Ray and what are the major differences when it comes to shadows and lighting?
V-Ray and Cycles use similar methods to light a scene (path tracing, global illumination). The differences is in their implementation and ease of use.
In cycles we define materials using "nodes". V-ray seems to take a more traditional approach in just having a giant material with lots of settings. Example would be to do a normal looking material in cycles, you have to mix diffuse with "glossy" shader. In Vray, glossiness is just a parameter for the material.
This allows cycles to have unique optimization strategies for rending, but it costs in its ease of use in my opinion.
Also cycles seems to be built for use on the GPU. It looks like V-ray has slightly more restrictions as to what is supported on the GPU compared to cycles (currently the only thing not supported on cycles GPU to my knowledge is subsurface scattering, which is on its way).
In the grand scheme of things, I think you could get 2 renders looking similar using both cycles and V-ray. V-ray has the advantage of money behind it, and I believe is more polished at the moment.