Which ocean is going to be swallowed by the Supercontinent Cycle, Atlantic or Pacific? The register shows several supercontinents have been formed on Earth's History:


  "The most recent supercontinent, Pangaea, formed about 300 million
  years ago (0.3 Ga). There are two different views on the history of
  earlier supercontinents. The first proposes a series of
  supercontinents: Vaalbara (c. 3.6 to c. 2.8 billion years ago); Ur (c.
  3 billion years ago); Kenorland (c. 2.7 to 2.1 billion years ago);
  Columbia (c. 1.8 to 1.5 billion years ago); Rodinia (c. 1.25 billion
  to 750 million years ago); and Pannotia (c. 600 million years ago),
  whose dispersal produced the fragments that ultimately collided to
  form Pangaea".
  
  Source: Supercontinent Cycle, Wikipedia


I would expect then a new supercontinent to form in some million years, but this implies Atlantic or Pacific Ocean, both with ocean-ridges and divergent margins, to disappear.

Wich one will be closed and wich one will survive to Supercontinent Cycle?
The pacific has already lost part its spreading center, north america has been pushed over it.. A few tiny non-contiguous plates like the  Juan de fuca plate is all that is left of the east pacific plate. in places like the san-andreas the north american plates has complete overridden the spreading center. 

In truth there are four possible predictions for the future: Novopangea, Pangea Ultima, Aurica and Amasia. two predict the atlantic disappearing one predicts the arctic and the final predicts the loss of the pacific. I think the latter two are more likely given what we see in the north america/pacific interaction but this is just opinion, the truth is we don't know a lot about how oceanic plates disappear or how spreading centers die because by their very nature they do not leave much evidence behind.