Mosquito-borne dengue (DENV) and Zika (ZIKV) viruses originated in Old World sylvatic (forest) cycles involving monkeys and canopy-living Aedes mosquitoes. Both viruses spilled over into human transmission and were translocated to the Americas, opening a path for spillback into Neotropical sylvatic cycles. Studies of the trade-offs that shape within-host dynamics and transmission of these viruses are lacking, hampering efforts to predict spillover and spillback. We infected a native, Asian host species (cynomolgus macaque) and a novel, American host species (squirrel monkey) with sylvatic strains of DENV-2 or ZIKV via mosquito bite. We then monitored aspects of viral replication (viremia), innate and adaptive immune response (natural killer (NK) cells and neutralizing antibodies, respectively), and transmission to mosquitoes. In both hosts, ZIKV reached high titers that translated into high transmission to mosquitoes; in contrast DENV-2 replicated to low levels and, unexpectedly, transmission occurred only when serum viremia was below or near the limit of detection. Our data reveal evidence of an immunologically-mediated trade-off between duration and magnitude of virus replication, as higher peak ZIKV titers are associated with shorter durations of viremia, and higher NK cell levels are associated with lower peak ZIKV titers and lower anti-DENV-2 antibody levels. Furthermore, patterns of transmission of each virus from a Neotropical monkey suggest that ZIKV has greater potential than DENV-2 to establish a sylvatic transmission cycle in the Americas.