This study presents results from 46 sensitivity experiments carried out with three structurally simple (2, 3, and 6 biogeochemical state variables, respectively) models of production, export and remineralization of organic phosphorus, coupled to a global ocean circulation model and integrated for 3000 years each. The models' skill is assessed via different misfit functions with respect to the observed global distributions of phosphate and oxygen. Across the different models, the global root-mean square misfit with respect to observed phosphate and oxygen distributions is found to be particularly sensitive to changes in the remineralization length scale, and also to changes in simulated primary production. For this metric, changes in the production and decay of dissolved organic phosphorus as well as in zooplankton parameters are of lesser importance. For a misfit function accounting for the misfit of upper-ocean tracers, however, production parameters and organic phosphorus dynamics play a larger role. Regional misfit patterns are investigated as indicators of potential model deficiencies, such as missing iron limitation, or deficiencies in the sinking and remineralization length scales. In particular, the gradient between phosphate concentrations in the northern North Pacific and the northern North Atlantic is controlled predominantly by the biogeochemical model parameters related to particle flux. For the combined 46 sensitivity experiments performed here, the global misfit to observed oxygen and phosphate distributions shows no clear relation to either simulated global primary or export production for either misfit metric employed. However, a relatively tight relationship that is very similar for the different model of different structural complexity is found between the model-data misfit in oxygen and phosphate distributions to simulated meso- and bathypelagic particle flux. Best agreement with the observed tracer distributions is obtained for simulated particle fluxes that agree most closely with sediment trap data for a nominal depth of about 1000 m, or deeper.