Neither one is used significantly more than the other, but 'start' is probably used slightly more often. They are both very common, and almost always interchangeable. The only difference is that 'start' can be used in combination with prepositions and adverbs, e.g. start off, start out, start up, start over, in ways that 'begin' can't. 'Start' also has an additional meaning of to set an engine in motion e.g. to start a car.

for present i use begin, to escape from boss i use " sir i have already started ! "