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The European Strategy for Particle Physics identified a high-energy e+e- collider studying the Higgs boson as the next priority collider project. The different proposals to realize such a collider all reach a similar performance on the core Higgs program at 250 GeV, albeit with different choices of luminosity and polarisation - but they differ in capabilities at lower and higher energies. This talk will review the physics capabilities of future e+e- linear colliders in the Higgs sector and beyond, with a specific emphasis illuminating the interplay of the top-level beam parameters luminosity, energy and polarisation.