One strategy for utilizing ammonia as an energy vector is to replace conventional hydrocarbons with hydrogen-enriched ammonia in existing or retrofitted combustors. However, the strong differential diffusion effect of hydrogen can significantly alter the combustion properties and cause challenges in combustor operability. Therefore, this numerical study performs a systematic investigation on the effect of differential diffusion on fundamental combustion properties of ammonia/hydrogen fuel blends. The investigated combustion properties span from the initiation of combustion, i.e., ignition, to stretched flame propagation and ultimately to flame stabilization mechanisms. The objective is to evaluate the feasibility of hydrogen/ammonia/air mixtures as substitutes for methane/air particularly considering the implications of differential diffusion effects. To this end, four fuel blends with similar unstretched burning properties are selected: fuel lean ammonia/hydrogen (AH-L), fuel rich ammonia/hydrogen (AH-R), fuel lean methane (M-L) and fuel lean methane/hydrogen (MH-L). First, the forced ignition and stretched flame propagation are evaluated. It is found that the AH-L (AH-R) mixture has a large negative (positive) Markstein length, and thereby among the selected fuel blends, AH-L (AH-R) has the lowest (highest) minimum ignition energy. Then flame stabilization mechanisms are investigated. For a stable flame, AH-L (AH-R) has an intensified (weakened) flame base and a weak (strong) flame tip, which shows a higher flashback (blow-off) propensity. Based on the critical gradient theory, a novel stability regime diagram is proposed. With the regime diagram, the flame stabilization limits (central flashback, boundary layer flashback, stable, and blow-off) and flow conditions can be determined for burners of different sizes.