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The high-Reynolds number stratified wake of a slender body is studied using a high-resolution hybrid simulation. The wake generator is a 6:1 prolate spheroid with a tripped boundary layer, the diameter-based body Reynolds number is $Re= U_\infty D/\nu = 10^5$, and the body Froude numbers are $Fr=U_\infty/ND=\{2,10,\infty\}$. The wake defect velocity ($U_d$) decays following three stages with different wake decay rates \citep{Spedding1997} as for a bluff body. However, the transition points among stages do not follow the expected $Nt = Nx/U_\infty$ values. Comparison with the wake of a circular disk in similar conditions \citep{Chongsiripinyo2020} quantifies the influence of the wake generator - bluff versus slender - in stratified flow. The strongly stratified $Fr=2$ wake is in a resonant state. The steady lee waves strongly modulate the mean flow and, relative to the disk, the $Fr=2$ spheroid wake shows an earlier transition from the non-equilibrium (NEQ) stage to the quasi-two-dimensional (Q2D) stage. The NEQ-Q2D transition is followed by a sharp increase in the turbulent kinetic energy and horizontal wake meanders. At $Fr=10$, the start of the NEQ stage is delayed. Transfers between kinetic energy and potential energy reservoirs (both mean and turbulence) are analyzed and the flows are compared in phase space (local Froude and Reynolds number as coordinates). Overall, the results of this study point to the difficulty of finding a universal framework for stratified wake evolution, independent of the features of the body, and provide insights into how buoyancy effects depend on the wake generator.