It is hard to say which is more powerful. Sure Kakashi can use it better than Sasuke, but when you look at Kakashi summoning the chidor even he has to hold his arm still from the shocks of holding that much chakra (I guess).
Look at Jairaya summon the Rasengan (in the manga), and *boom*, instantaneous. No burnt hands, no two-handed style ala Naruto, no holding his arm down to contain the chakra, and not obvious what he was about to do.
Sure, Jairaya is a legendary ninja, and sure Kakashi could attain Jairaya's level (good luck) and then create the chidory faster. The two, however, are probably for different purposes, though an assassination weapon (chidori) that sounds like 1K birds isn't exactly silent, is it, but it is effective...as far as we're told.
The Rasengan, when done right, is almost undetectable as Jairaya uses it, and destructive. As far as matching personality types...was the 4th like Jairaya and Naruto?