Epitaxial recrystallization of amorphized mono- and multi-elemental semiconductors can be induced by MeV ion irradiation at temperatures where the rate of thermally induced recrystallization is negligible. For the present report, ion-beam annealing of InP and GaAs is compared. Amorphous surface layers of thickness approximately 95 nm were formed by 50 keV Si ion implantation at a temperature of approximately -196-degrees-C and epitaxial recrystallization was subsequently achieved with 1.5 MeV Si ion irradiation at 160-degrees-C. The extent of recrystallization was determined from Rutherford backscattering spectrometry/channeling and in-situ time-resolved reflectivity measurements. Residual disorder has been characterized with transmission electron microscopy. At a given irradiation temperature and MeV Si ion dose rate, significantly different modes of ion-beam induced recrystallization are apparent for InP and GaAs. For both materials, ion-beam annealing suppresses the onset of the twinned regrowth characteristic of thermal annealing, though the extent of single-crystalline regrowth is greater for InP. Microtwins and dislocations are observed in ion-beam annealed InP layers, but the size of microtwins is reduced from that observed in thermally annealed samples. For GaAs, single-crystalline regrowth is apparent for only approximately 20 nm following which a rapid ion-irradiation induced, amorphous-to-polycrystalline transformation is observed over the remaining approximately 75 nm of material.