The effect of polymer architecture on molecular exchange in block copolymer micelles has been investigated using time-resolved small-angle neutron scattering (TR-SANS). Narrowly dispersed symmetric PEP-PS-PEP and PS-PEP-PS triblock copolymers were synthesized, where PS and PEP refer to poly(styrene) and poly(ethylene-alt-propylene), respectively. Spherical micelles of the triblocks in squalane, a selective solvent for the PEP blocks, were prepared using a cosolvent method. PEP-PS-PEP forms hairy micelles with the PS blocks looped in the cores, while PSPEPPS forms flower-like micelles with most of the PEP blocks looped in the corona. The micelle structure was characterized by small-angle X-ray scattering, providing in particular the core radius as a function of temperature. TR-SANS experiments were conducted on solutions containing 1 and 6 vol % PEP-PS-PEP, and 0.25 and 0.5 vol % PS-PEP-PEP, using matched pairs of deuterium-labeled (dPS) and normal (hPS) specimens and a mixture of normal and perdeuterated squalane contrast-matched to uniformly mixed hPS/dPS micelle cores. Blends of micelles with initially pure hPS and dPS cores produce scattering intensity that decays with the redistribution of block copolymer chains as a function of time, providing direct access to the rate of molecular exchange. Remarkably, the two triblock architectures display exchange rates that differ by approximately 9 orders of magnitude, even though the solvophobic PS blocks are of comparable size. This discovery is considered in the context of a model that successfully explained the exchange dynamics in PS-PEP diblock copolymer micelles.