The French model of absolutism entailed putting all affairs of the state solely in the hands of Louis XIV whereas Frederick William the Great Elector dedicated his efforts to building a strong military and bureaucratic foundation in Prussia; Peter the Great was more interested in bringing western reforms to Russia.
Louis XIV strengthened the power of the monarchy by spending a large amount of resources in building the vast grounds and palace of Versailles, which would be both his home and the location where all policy decisions would be made. While Louis made decisions over foreign policy, the Church and taxes he was able to keep an eye on the nobles who would vie for his attention in the hopes of seeking higher office, or pensions. While enjoying hunting trips, gambling, and other entertainments at Versailles they would trip over themselves to dress the king when he awoke, or to sit next to him during a meal. Louis used these court rituals and etiquette as a symbolic gesture of his power over the nobles. Though he effectively kept the nobles distracted from his governance, the Sun King, as he liked to call himself, left France in great debt.
In Prussia, Frederick William invested heavily in building the army to defend the country but also to strengthen his rule. Because of his efforts, the Prussian army earned the reputation as being one of the best equipped, well trained and fourth-largest in Europe. Unlike Louis XIV who preferred to distract and distance the nobles from political affairs, Frederick invited the Junkers (Prussia's landed aristocracy) to play a role in the newly created Commissariat - the agency tasked with generating revenue and overseeing the growth of the army. This institution would eventually be used to govern Prussia.
Peter the Great was able to strengthen his rule as a consequence of his greater interest in modernizing Russia and opening it up to the West. He reorganized the army employing both Russians and Europeans as officers, as well as forming the first Russian navy based on European technology. He also successfully defeated Sweden in a battle to control the Baltic coast where he began the construction of the new capital St. Petersburg. This was intended to serve as Russia´s "open window to the West". These accomplishments not only helped improve Russia geopolitical position in relation to Europe but also reinforced the role of the monarchy.
Because of these varying absolutist styles by the time Louis XVI comes to power in the late 1700s France will see a revolution, while the monarchs of Prussia and Russia will still be entrenched in their positions.
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References:
Glencoe World History - Jackson J. Spielvogel
