Block copolymers can exhibit a pronounced yield stress, but the impact of molecular architecture, chemistry, and self-assembly on macroscopic rheology remains poorly understood. Here, we study the linear-viscoelastic and yield-stress fluid behavior of two architectures—bottlebrush copolymers (with statistical or blocky sequences) and linear diblocks—that self-assemble into body-centered cubic (BCC) spheres and hexagonally close-packed cylinders (HEX). The dynamic properties of these polymers were probed by oscillatory frequency and amplitude sweeps at temperatures well below the order–disorder transition (TODT) to furnish insights into the yielding transition. All BCC-forming polymers have a similar signature of yielding: smaller yield strains (γy,BCC ≈ 0.053 < γy,HEX ≈ 0.18), sharper solid–liquid transitions, and better reversibility than HEX. Statistical bottlebrushes show the most frequency-independent structural modulus (G0) and no signs of defect relaxation. A simple power-law relationship captures the dependence of the normalized structural modulus (G0/RT) on the inter-micelle distance (d) across different architectures and morphologies [G0/(RT) = 1.31 × 104 (nm2.6 mol/m3) d–2.6]. These studies establish quantitative structure–property relationships that are relevant in contemporary applications, for example, extrusion-based 3D printing.