In this paper, we present a comparison between our recently published randomized version of the finite set statistics (FISST) Bayesian recursions for multi-object tracking with the commonly known Hypothesis Oriented Multiple Hypothesis Tracking (HOMHT) method. We start by revisiting our hypothesis level derivation of the FISST equations in order to appropriately introduce our randomized method, termed randomized FISST (RFISST). In this randomized method, we forgo the burden of having to exhaustively generate all possible data association hypotheses by implementing a Markov Chain Monte Carlo (MCMC) approach. This allows us to keep the problem computationally tractable. We illustrate the comparison by applying both methods to a space situational awareness (SSA) problem and show that as the number of objects and/or measurement returns increases, as does the computational burden. We then show that the RFISST methodology allows for accurate tracking information far beyond the limitations of HOMHT.