See the elevation difference between the base points of both sides. The Somwarpet side is already at about 1100 m elevation, making the further climb less strenuous. So is the distance to the KP peak from earthier side. From Subrahmaniya side you'll reach the peak after 14km of trek whereas from the Beedehalli (Somwarpet) side it is almost half as long.

The 14km trail from Kukke to Kumara Parvatha peak is all about scaling 1½km (about 1500 m/4930 feet) in elevation. From the Beedehalli you'll reach the Kumara Parvatha peak after 600 meters of elevation over a 7km long trek. That's Beedehalli is already at an elevation of 1100 meters, where as Kukke is about 140 meters.

So from a difficulty scale the Beedehalli to Kumara Parvatha peak fares better (or less challenging, if you're an avid climber!)