We study the scattering of two boson stars by comparing four sequences (at fixed energy and varying impact parameter) of numerical relativity simulations to an effective-one-body analytic description, taking into account both gravitational effects (point-mass and tidal) and short-range scalar-field interactions. We obtain excellent agreement between analytical and numerical results, exhibiting the importance of short-range scalar-field interactions for small impact parameters. Our Letter paves the way toward analytic waveform templates of exotic compact object binaries.