generally second to the Fatimids early on
This is where I have to disagree. The Byzantine Navy was intermittently the dominant force in the Eastern Mediterranean (including the Adriatic) and Black Seas whenever the Empire needed to project its power to secure commerce between Dalmatian city-states up until the mid 11th century. The decline of the Byzantine Navy coincided with the decline of its necessity. For centuries after the rapid expansion of the Islamic Caliphates, several attempts at invading or conquering Constantinople were thwarted or driven back by the Imperial Fleet coordinating with Thematic Navies, yet Arab raids still remained a thorn in the Empire's side until... the mid 11th century. With this, the need for the Byzantine Empire to project power abroad was marginal, the Empire grew complacent with its secure position, its themes ceased to undertake any significant campaigns, and all were looking increasingly inward. The only notable campaigns of this period (1025-1071) were in Armenia and Sicily (the Emirate, not the soon to be Norman kingdom).
The Empire became more reliant on both the Tagma and Imperial Fleet based in Constantinople under direct Imperial oversight, and the Constantinopolitan bureaucracy, increasingly at odds with the military high command, sought to weaken their influence. The neglect of the military aristocracy that had provided the Empire with such impeccable leadership on the frontier in favor of central reserve forces in the capital deprived it of effective and immediate defenses, particularly in Anatolia, combined with the integration of Armenian buffer states into the Empire and commuting military service for payment left Anatolia wide open.
These are all developments that came nearly 2 centuries after the establishment of the Fatimid state. The Fatimid Navy only came in contact with the Byzantine Navy briefly after the Fatimids expanded into Egypt and founded Cairo, and from then until around 1000 it was primarily used to defend Fatimid rule in coastal Levantine cities, to mixed results. The Byzantine Navy was beginning its medieval apogee just as the Fatimids were done with their conquest of Egypt.
never truly dominant during the CK2 period
See above.
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