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Due to thermohaline circulation, the Pacific water is more 'aged' so there is a higher amount of total dissolved inorganic carbon (e.g. CO2) in the deep Pacific when compared to the Atlantic. However, I don't know how this affects the relative 13C/12C enrichment of the Pacific. Factors I've thought about:

  1. Oxic respiration of buried organic matter is the source of CO2 in the deep ocean.
  2. Deep Pacific water has accumulated more respired CO2 since the Pacific is at the end of the deep circulation.
  3. Algae and microbes fractionate against 13C in favour of 12C.
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"The decrease in δ13C as water flows from the Atlantic to the North Pacific is due mainly to the addition of organically produced material and its subsequent oxidation as it falls through the water column. Marine organic carbon has a δ13C of near -250/00, hence the addition of this material decreases the δ13C of the ΣCO2." (from conclusion)

P. M. Kroopnick, Deep-Sea Research Part a-Oceanographic Research Papers, 1985, 32, 57-84. https://www.sciencedirect.com/science/article/pii/0198014985900172

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