Off-grid energy systems provide energy to remote communities that lack basic energy infrastructure. Designing 100% renewable energy-based off-grid systems contributes significantly to decarbonization while achieving United Nations Sustainable Development Goals. Such off-grid energy systems where solar and wind provide all the primary energy, incorporating uncertainties for solar irradiation, wind speed, and ambient temperature influences the optimal system design. This paper compares Stochastic Programming (SP) and Robust Optimization (RO) design logic to optimize the off-grid system size subjected to weather uncertainties. SP considers the probability of various weather scenarios, while RO focuses on the worst-case scenario. This creates a trade-off: SP offers potentially lower costs but might not perform in the worst-case, while RO prioritizes reliability at the expense of potentially higher costs. To compare SP and RO design logics, this paper develops a stochastic multi-objective modelling framework for a case study involving solar, wind, heat pumps, and various storage options (electric, thermal, and hydrogen). The expected results are cost curves depicting the trade-off between system cost and security of supply for each design logic. This will provide valuable insights for policymakers in balancing cost, reliability, and risk tolerance when designing off-grid renewable energy systems.