CHIDORI. It looks cooler. It sounds cooler. It's more useful, more practical. It's more versatile. It's more lethal, a killer, a "weapon of choice for assassination".
Rasengan holds more punch and has greater destructive power but Chidori is sharper and has superior piercing power. Rasengan is a showy smasher, Chidori is a stealthy blood spiller. They both have usefulness in different cases, Rasengan is useful for destruction (for example Naruto destroyed Shinno's flying fortress in the movie Bonds, Chidori couldn't do that on similar level) but Chidori has the slight edge in battle (Chidori's killing power is greater than Rasengan, Minato could do nothing to Obito after smashing a big Rasengan but destruction was greater whereas Chidori went right through his heart and could've killed him if he was normal) IMO. Plus, its versatility just takes it to a new level against Rasengan.
I would happily wield any of them since they are both powerful and awesome, but if given a choice, Chidori will be my priority.
BTW, I'd prefer to be hit by a Rasengan over Chidori. Breaking a few bones is preferable than death.
Shape transformation can be considered a part of normal version since it changes form based on the original technique's pureness. Nature transformation is different since other elements are involved.