Pixar is the animation studio producing the biggest animated movies for many years and continue to do so. Inside Out, Toy Story, Finding Nemo, Brave, The Good DInosaur, are just a few of the more recent movies they have made and the list goes on and on. Pixar animations does incredibly beautiful and touching productions and deserves to be acknowledged.
To clarify, I don't believe that Pixar alone is the greatest animation studio of all time; however, since combining with Disney I believe they are arguably the greatest of all time. Disney has by far been the first and most prolific of animation studios in the world. It brought us classics that we grew up watching and that our children and grandchildren will watch for years to come. Combined, Disney-Pixar will lead the way into the future of animation.
Pixar has done a lot of great work over the past decade or two, but it cannot quite compare to the nearly hundred years of work by studios such as Disney and Warner Brothers. Give Pixar another 20 years, and perhaps they'll be the best then. At present I'd have to go with Disney.
Now, there's no doubt in my mind that Pixar will eventually overtake everyone but for now I still believe Disney is still the best animation studio. Disney unfortunately are still relying on the oldies but goodies and are trying to find the next best thing, while Pixar seems to just keep rolling out winners one after the other. They are sill a pretty new company so they still have to show respect to the original.