We investigate the statistical variability of the threshold voltage and its sensitivity to critical geometrical parameters in ultrascaled In0.53Ga0.47As and Si MOSFETs by means of 3-D quantum-corrected drift-diffusion simulations. Dual-gate ultrathin-body and FinFET device structures are analyzed for both channel materials. To assess the variability and sensitivity effects also from the scaling perspective, we consider devices belonging to two technological nodes with gate lengths 15 and 10.4 nm, designed according to International Technology Roadmap for Semiconductors (ITRS) specifications. Variability sources included in our analysis are random-dopant fluctuation, work-function fluctuation (WFF), as well as body- and gate-line-edge roughness (LER). Sensitivity to critical geometrical parameters is assessed by varying gate length, channel thickness, and oxide thickness. Results point out the major detrimental effect of WFF and Body-LER for InGaAs FETs, whereas WFF dominates in Si counterparts. Moreover, the sensitivity analysis shows that control over gate length and channel thickness in the InGaAs technology is fundamental in order to keep variability within tolerable values. Scaling of the InGaAs technology highlights the importance of abiding to ITRS projections regarding LER control improvement. Furthermore, a tight channel thickness control is required in ultrascaled devices due to the large sensitivity of the threshold voltage to the channel thickness combined with increased variability