In this work, we present the chain exchange kinetics in block copolymer micelles of spherical and cylindrical geometry. The aim of this work was to understand the mechanisms controlling the molecular exchange with a particular focus to delineate any potential effect of the micellar morphology. As model system symmetric short-chain amphiphilic poly(ethylene-alt-propylene)-poly(ethylene oxide) diblock copolymer (PEP1-PEO1, numbers denote approximate molecular weight in l(D) in aqueous solutions has been used. This system undergoes a irreversible cylinder to sphere transition upon addition of N,N-dimethylformamide (DMF) as cosolvent or upon heating. This feature allowed to quantitatively compare chain exchange kinetics in both morphologies. The kinetics were accessed by using hydrogen/deuterium labeling and time-resolved small-angle neutron scattering experiments employing a stopped flow apparatus by which the kinetics could be followed from about some hundreds of milliseconds up to hours. The results show that, independent of morphology, all data can be satisfactorily described by a scaling model that takes into account the polydispersity of the core forming PEP block in order to describe the broad logarithmic time decay at longer times. A small but significant effect of the morphology could be seen which was reflected in a slightly accelerated kinetics for spherical micelles. A detailed comparison shows that for both morphologies, the activation energy follows a scaling law proportional to the product of the interfacial tension, gamma, and the number of repeat units of the, insoluble block, N(B), i.e., E(a) similar to gamma N(B) rather than the gamma N(B)(2/3) predicted by Halperin and Alexander. This implies a stretched conformation of the insoluble block during the expulsion process compared to the more globular shape considered in the original scaling theory. This can be related to insufficient chain length/statistics for these rather small chains to form a globule during the expulsion process; or to an higher polymer density within the corona of these "crew cut" type micelles. Through the analysis, the faster kinetics could be summarized in a slightly smaller activation energy for the spherical micelles which is probably related to small changes in the internal corona structure.