The migration to the Terahertz (THz) band and the deployment of extremely large antenna arrays (ELAAs) are transitioning wireless communications into the radiative near-field regime, fundamentally evolving conventional angular beam steering to beamfocusing (BF). However, the combination of the extremely narrow beamwidth and the mobility of the users necessitates frequent beamfocusing reconfigurations, incurring a significant switching overhead that degrades the system achievable throughput. In this regard, caustic beamforming (CB) is a promising alternative based on the synthesis of a continuous curved beam, which eliminates the need for beam tracking at the expense of a distributed beamforming gain. By leveraging the Airy beam as a canonical model, this paper develops an analytical framework to compare the throughputs achieved by CB and BF. Our main results include closed-form throughput expressions for both beamforming strategies and a performance boundary for paradigm selection. First, we derive the BF throughput by modeling a defocusing penalty induced by continuous user movement. The optimal beam dwell time that maximizes the throughput is analytically determined, and the impact of user speed and switching overhead on the throughput is quantified. For the CB scheme, we demonstrate that its throughput is determined by the signal-to-noise ratio (SNR) and the geometry of the trajectory of the user, yet invariant to the user speed. Finally, we analytically establish a threshold for the switching overhead to define the crossover point of the achievable throughput of both beamformers. Crucially, this threshold asymptotically vanishes at extremely high frequencies, positioning the continuous CB scheme as the preferred beam design paradigm for high-mobility THz communications.