Dual agent dose-finding trials study the effect of a combination of more than one agent, where the objective is to find the Maximum Tolerated Dose Combination, the combination of doses of the two agents that is associated with a pre-specified risk of being unsafe. In a Phase I/II setting, the objective is to find a dose combination that is both safe and active, the Optimal Biological Dose, that optimises a criterion based on both safety and activity. Since Oncology treatments are typically given over multiple cycles, both the safety and activity outcome can be considered as late-onset, potentially occurring in the later cycles of treatment. This work proposes two model-based designs for dual-agent dose finding studies with late-onset activity and late-onset toxicity outcomes, the Joint time-to-event (TITE) partial order continual reassessment method and the Joint TITE Bayesian logistic regression model. Their performance is compared alongside a model-assisted comparator in a comprehensive simulation study motivated by a real trial example, with an extension to consider alternative sized dosing grids. It is found that both model-based methods outperform the model-assisted design. Whilst on average the two model-based designs are comparable, this comparability is not consistent across scenarios.