They are both lethal techniques.
The Chidori is classified as an assassination move. It can puncture it's target in a blink of an eye and kill them before they can even react. This is mentioned by Gai during the Chuunin Finals and demonstrated by Kakashi versus Kakuzu.
The Rasengan is the pinnacle of shape manipulation and delivers enough force to seriously damage it's opponent.
You can compare the two techniques like this:
-The Chidori is like a knife or a blade
-The Rasengan is like a sledgehammer
Both of these weapons are different in appearance and use, but they can both kill you in 1 hit.
As for which one's better, I would go with the Rasengan. Why? Because it doesn't have an elemental disadvantage like the Chidori. Both are powerful techniques, but the Chidori can't be used against a Wind-user because it'll be mercilessly countered. The Rasengan on the other hand can, in theory, be used against anyone because it's composed of normal chakra.
Everyone who's bringing up the Rasenshuriken or other variants of the Rasengan are wrong. Those are derived from the Rasengan, but they are not the Rasengan. The Rasengan is in reference to the original base version. Even the Oodama Rasengan is technically not the same as the Rasengan. It may just look bigger, but by definition it is a different version.
The Chidori also has variants like the Chidori Senbon, Chidori Nagashi, Sasuke's Chidori Spear, and Kakashi's Lightning Transmission. Yet, they are not the same as the Chidori, the original base version. So stop bringing them into this discussion.