The left atrium and left ventricle represent the workhorse side of the heart, which accepts oxygenated blood from the pulmonary veins and then pumps it throughout the body to all the organs and tissues that need it. This also means the walls of the left side of the heart muscle are up to five times thicker than that of the right because they have to pump blood at higher volumes and pressures.
So it follows that a heart attack centered on the left side of the heart puts major organs and tissues at risk, while a heart attack on the right side jeopardizes the ability of the body to re-oxygenate blood. To be sure, neither kind of heart attack is good, and both are dangerous, but a left side heart attack is thought to be more dangerous.
From a surgical standpoint, operating on the left side of the heart is sometimes considered more difficult given wall thickness and organ function.