Anton and the Battle by Ole Konnecke shows the boys one-upping each other. This book takes a a brothers argument or neighborhood friends having a squabble and infuses imagination into it.
One is louder than the other, stronger, and it escalates until a small dog comes along. Luke and Anton, both are afraid of the dog.
From Wikipedia: Konnecke is a German illustrator and his art has a cartoon style.
This story could be used during a Play Storytime, Pretend or just Imagination. Young children would just love to tell you their whopper story!
The best part is after they get away from the dog, he comes after them again, then Luke and Anton are in cahoots against the dog, back to being friends!