Shinobi using Rasengan can often use it more times in a battle as compared to a shinobi using Chidori. Kakashi on one hand, could only use Chidori upto a maximum of four times a day in Part 1. Naruto, however, even when he is using Shadow clones (meaning that he would have only a fraction of the chakra he normally has) still has no trouble using the Rasengan more than that and still have plenty of chakra.
The Rasengan is almost equally, if not more, powerful than the Chidori. So the Rasengan should require the same or more amount of chakra than the Chidori. Naruto is also said to be very inefficient in using jutsu. So even though he has more chakra than Kakashi, his Rasengan would be less efficient than Kakashi's Chidori. I do not believe that Naruto chakra levels are so vast, that even with the use of shadow clones and being inefficient while using jutsu, he can use it multiple times while still retaining plenty of chakra.
So why can Naruto use the Rasengan more than Kakashi using the Chidori?