Rasengan is less complicated than Raikiri/chidori, simply because rasengan only use shape manipulation to its highest degree while raikiri uses shape manipulation and nature manipulation of lighting.
I do not belive that Kakashi knew rasengan when he was a kid, I believe Kakashi learned how to do it when he was on countless missions with Naruto.. I mean how can Kakashi not understand how to do rasengan after seeing it a dozen times Naruto using it? Thus Minato never tried or taught Kakashi rasengan.
Conclusion: Chidori is not watered down version of Rasengan the jutsus are somewhat equal but rasengan can beat chidori if yo increase its rotation speed and size... I'm sure you have seen it dozen times when Naruto and Sasuke clashed with both jutsu. Well rasengan is an exploding type power while chidori is a penetrating/ piercing type.. see the difference there???
