Rasengan is better, it doesn't require hand signs, it have very good destructive power and it can be combined with an element to get a whole new technique.
While chidori have its own advantages, like it is much more effective against suiton,nullify raiton attacks and once perfected it can be used to unlock new techiniques such as chidori nagashi,chidori sword etc. And it looks more badass than a rasengan.
I would choose chidori over rasengan