How do AMD chips compare to Intel chips for VFX rendering?

Are you asking about GPU or CPU? And is it the viewport rendering performance or the Final Render of your work? NVidia graphics cards tend to have better openGL drivers. Maya viewports run on both DX and OGL. To run Maya any good graphics card will do the job, of course they need to have good drivers which AMD don't seem to produce often. I can tell from personal experience that even the FirePro from AMD has glitches appearing randomly  with certain OGL softwares. I had used one with updated drivers and it still glitched out. I have both NVidia and AMD on my two machines and both of them are gaming GPU's. They perform quite well. With some occasional glitches with the AMD's card. If you are asking for performance of CPU's with renderers like Arnold, Renderman,Mental Ray, VRay, Maxwell etc you can search for various benchmarks for both AMD and INTEL. With CPU renderers the more processors you have the better. There are a few GPU renderers like Redshift, Octane, Furyball etc that utilize the Graphics processor of your computer, and are very fast than traditional CPU renderers. Most of them requires NVidia cards though. GTX Titan or any card from GTX series with 2 GB or more memory will work. Hope it helps. Cheers.

In my experience they both work fine, but Intel and NVidia have more specialized equipment which will work better such as the Intel Xeons and NVidia Quadros.  Most professional companies including Pixar use Nvidia GPUs which carry most of the rendering load, I'm not sure what CPUs they use, but that isn't as important. http://blogs.nvidia.com/blog/2014/03/26/how-pixar-uses-gpus/

Intel chips performs quite a lot faster during renders, if you skip the price tags.

Nvidia as it renders tesellation better, I have a 1GB AMD graphics but i m facing problems which are not there while i was using 512MB Nvidia