During inspiration, venous return to the right ventricle is augmented because of increased negative intrapleural pressure. As a simple Frank-Starling effect (increased preload -> wall stretch), stroke output from the right ventricle is increased. At the same time, stroke output from the left ventricle is decreased as the expanding lungs momentarily hold the blood.
Leftward movement of the interventricular septum also somewhat limits left ventricle filling. The net effect is a fall in arterial blood pressure and increase in heart rate during inspiration.
During expiration, just the opposite occurs. This phenomenon is known as "inspiratory tachycardia" or "sinus arrhythmia". Over a period of many seconds or minutes output from the right and left hearts is, of course, equal.