According to some guy on /m/….
It appears to me that Ren and Stimpy at the American equivalent of Neon Genesis Evangelion.
Evangelion’s success was due largely to its strong characters, who were humanized forms of standards in anime of the day such as the tsundere or yamato nadeshiko. Those personalities were shown disturbingly to have had an origin which led to their formation, and the events around them cause them to contort. Ren and Stimpy does not possess a format that allows this, but at the same time delivers a human grit to the characters that was yet to be seen. Some characters were at times malicious, a far uglier and more truthful display than the playful violence shown in golden age cartoons. Other characters are merely irresponsible – the only ones who can ever truly be good are the ones who are too stupid to be anything else. While at times Ren and Stimpy shows the true cruelty of classic cartoon characters, it is mostly the surreal universe that shows the sad display. In an existential way, the existence of the bizarre in the universe has no purpose and does not serve anyone, often leading Ren and Stimpy to their deaths for no good reason. Like in Eva, a broken world filled with broken people cannot fix itself.
I can sort of see some similarities between Asuka and Ren. They’re both cruel to the person they view as lesser to them, perhaps knowing that that person has more potential. They both demand to take the lead and be praised as the superior one, though Ren tries to pull Stimpy back whereas Asuka merely pushes herself away from others. Not to mention that they’re both simply unbalanced.
In brief, Evangelion brings a psychological tone of a certain level to anime, while Ren and Stimpy brings it to Western animation. Their influence, however, was limited to thin robots and psychobabble or gross-out humour.