Neon genesis does have a complex storyline, for example,the Angels are alternate forms of humanity,which seek lillith,the giver of life,while the Evangelions,clones of adam,the first human try to prevent the various angels from reaching their goal,using the Absolout Terror field,not known to man but the feild that keeps your mind seperate from others,which will erode if lillith comes in contact with the angels or adam, which is why SEELE made the evangelions,to initiate this erosion by merging one of them with lillith, to "re-build" the human race(third impact) contrary to Gendo Ikari's plan to initiate third impact so he can re-unite with his wife,who had perrished in second impact, (when SEELE had tried to shrink adam into an embreonic form for transportation and genetic experiments.Gendo had adam implanted in his hand so that he could initiate third impact by berging it with Rei, the first child(first Evangelion pilot) who his a clone of Yuri Ikari,Shinji's mother,with the synthesised soul of lillith.
Each evangelion has the soul of the parents mother absorbed into it,as it is a clone of a human without a soul, EVA 00 has Ritsuko's mother(the cheif programmer of the EVA project)which is why Rei allways has trouble piloting it,while EVA 01 has Yuri's soul in it and EVA 02 has Asuka's mother's soul in it, which is why half way through the series Asuka loses her sunc ratio with it, because she has deep seeded isues with her mothers suicide (she went crazy when she lossed her soul to EVA 02).
So there. not complex enough for you? I could go into further detail !