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As energy systems decarbonize, managing renewable variability becomes critical. Storage technologies such as battery energy storage systems (BESS) and hydrogen are often expected to play complementary roles across different timescales. However, the extent of their substitutability remains unquantified. To address this, we model the stochastic long-run equilibrium of an integrated electricity-hydrogen system in Germany using the Stochastic Dual Dynamic Programming (SDDP) algorithm. We quantify the economic interplay between BESS and hydrogen using the Morishima elasticity of substitution. Results indicate they act as imperfect economic substitutes rather than complements. A 1% reduction in BESS costs lowers hydrogen-to-BESS investment ratios by 2.3–3.1%. This displacement is absolute, not merely relative, as halving BESS costs reduces electrolysis, hydrogen storage, and hydrogen turbine capacities by 18%, 50%, and 77%, respectively. While hydrogen offers high energy-to-power ratios that BESS cannot provide to substitute for gas-fired plants, we show that the bulk of hydrogen’s flexibility value lies in services that significantly overlap with BESS capabilities. These findings reveal a previously underappreciated risk to hydrogen deployment arising from direct economic competition with batteries. • A stochastic model for investment and dispatch in an integrated electricity- hydrogen system. • Interaction between batteries and hydrogen technologies is investigated. • Battery can partially substitute for hydrogen, and vice versa. • As battery costs decline, the economic relevance of hydrogen shrinks.