The best statement that 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 monarchs took towards their authority and governance. While Louis XIV emphasized the grandeur of his reign and maintained a façade of absolute power, Peter the Great undertook substantial reforms and displayed more direct control over the state, aligning more closely with the principles of true absolute rule.