The statement that best compares the absolutism practiced by Louis XIV and Peter the Great is:
Louis XIV created the illusion of absolute power, while Peter the Great was closer to a true absolute ruler.
This statement highlights the different approaches both rulers took in consolidating their power. Louis XIV is often seen as having maintained a facade of absolute power by centering his reign around personal magnificence and the spectacle of his court at Versailles, while Peter the Great enacted significant reforms and exercised more direct control over government and military, establishing a more tangible form of absolute rule in Russia.