From Dravidian Etymological Dictionary.
PDr *k- is palatalized in Tamil before front vowels (an approximate statement); Tamil, therefore, in many forms has the initial phoneme c- when the reconstructed PDr form would have k-.
From the following table, its evident that Kannada preseves Proto Dravidian's (PDr) *k- as it is whereas Tamil has switched to 'c-'
Compiled from Dravidian Etymological Dictionary
However, when 'k' is followed by pattern [front vowel][retroflex], switching to 'c-' doesn't occur in Tamil.
Kannada Tamil English
kēḷ kēḷ to ask, to hear
Here ē is front vowel
ḷ is a retroflex