We consider a spinning test-body in circular motion around a nonrotating black hole and analyze different prescriptions for the body's dynamics. We compare, for the first time, the Mathisson-Papapetrou formalism under the Tulczyjew spin-supplementary-condition (SSC), the Pirani SSC and the Ohashi-Kyrian-Semerak SSC, and the spinning particle limit of the effective-one-body Hamiltonian of [Phys. Rev. D.90, 044018(2014)]. We analyze the four different dynamics in terms of the ISCO shifts and in

more »

... rms of the coordinate invariant binding energies, separating higher-order spin contributions from spin-orbit contributions. The asymptotic gravitational wave fluxes produced by the spinning body are computed by solving the inhomogeneous (2+1)D Teukolsky equation and contrasted for the different cases. For small orbital frequencies Ω, all the prescriptions reduce to the same dynamics and the same radiation fluxes. For large frequencies, x ≡ (M Ω)^2/3 >0.1 , where M is the black hole mass, and especially for positive spins (aligned with orbital angular momentum) a significant disagreement between the different dynamics is observed. The ISCO shifts can differ up to a factor two for large positive spins; for the Ohashi-Kyrian-Semerak and the Pirani SSC the ISCO diverges around dimensionless spins ∼0.52 and ∼0.94 respectively. In the spin-orbit part of the energetics the deviation from the Hamiltonian dynamics is largest for the Ohashi-Kyrian-Semerak SSC; it exceeds 10% for x>0.17. The Tulczyjew and the Pirani SSCs behave compatible across almost the whole spin and frequency range. Our results will have direct application in including spin effects to effective-one-body waveform models for circularized binaries in the extreme-mass-ratio limit.