And when it comes to the old stuff, Disney is clearly the king in terms of animation movies.

The REALLY old stuff, yes. Disney reigned in the 40s and 50s, and 60s to a lesser extent. By the 70s, Soviet and French animators were surpassing Disney, and Japan has been the unrivalled king of feature length animation in the life of anyone born since the 80s. As enduringly popular as a couple of the '90s Disney renaissance titles have been, the only one to receive unanimous praise is Beauty and the Beast, whereas that amount of acclaim was received by a dozen different Ghibli productions (like Disney, and unlike other anime, these are mostly aimed at families/kids). Ghibli, not Disney, is the norm for most millennials and younger.