Ransengan is better. It's fact even Kakashi says it him self. But when it comes to black chidori that's better, but the Ransen-Shuriken(wind element ransengan) beats that.
Come on guys, apples and oranges.* Chidori was created as a technique for assasinations.* It can cut through anything, but it is a straight forward thrust, and is easily countered.* I mean come on, you can see it coming a mile away, and even hear it from that distance.* Rasengan, on the other hand is a technique for close combat, which requires not signs to use for its execution.* A finishing-blow taijutsu technique, the equivalent of a right-cross in boxing.* Sure it can be countered, but with the right set-up, it is impossible to stop.* On the other hand, you only know after it hits if you have done enough damage to kill your opponent, while the Chidori will cut through flesh, into or through the person's chest, not simply knock them away.* Depending on your needs, you would go with one over the other, though a prefer myself the Rasengan due to its quick execution and level of damage.