Disney has the best movies of the bunch outright, their best are not just among the best animated movies ever made, but among the best films ever made.
Dreamworks is the most consistent and a solid 2nd place, fantastic at making sequels that actually improve upon their predecessors like Kung Fu Panda 2 or Shrek 2 and they also have absolute classics like Prince of Egypt and The Road to Eldorado.
Pixar WAS very consistent and also have a fair few really good films but they've fallen off the rails a bit recently and now it's a bit of an ups and downs situation with regards to how good their films end up being. I will say they are the best at evoking the feels.
The Disney classics are hard to beat; but, there are some really great Pixar movies too. Toy Story, Cars, Monsters Inc, Wall-E, The Incredibles. I could go on. If we're basing it off current stuff, then Pixar gets my vote.
favorite regular disney movie is fantasia which is pretty important to me but loses out to toy story
I do enjoy the how to train your dragon movies and shrek and stuff but they definitely didn't have the same impact (and I was already a teenager by the time httyd started)