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They corrected the errors of the Byzantines: under Komnenoi byzzies turned state aparatus into family mafia undermining the reasonably meritocratic state in return of short-term increase of power - the long term result was corruption and lessened efficiency, as well as a rise of a pretty big extended family of oligarchs with claims to the trone. One of the reasons why Byzantium was so powerfull at its peak was the very efficient tax system and beaurocracy which allowed that divide and rule and famous byzantine diplomacy.
Ottomans were smarter and while remaining dynastic state they nonetheless managed to undermine lower family and relatives from getting too much power. If you think of it Janissary system (and state schools for administration they attended) it is evolution of the idea behind Varangian guard - you take "foreigners" into your court so they depend on the ruler only as they don't have any other powerbase.
This of course degenerated with time as it became possible for the children of Janissaries to get high positions in the court which removed the main advantage of the system. But for a time it allowed for every efficient centralised system of governance.