Typical high-energy negative ion electrostatic accelerators such as the ones designed for fusion applications produce a significant amount of secondary particles. These particles may originate from coextracted electrons, which flow from the ion source, impacting the accelerator grids or as by-products of collisions between accelerated negative ions and the residual background gas, in the accelerator. Secondary emission particles may carry a non-negligible power and consequently must be precisely studied. The electrostatic-accelerator-Monte-Carlo-simulation code (EAMCC) [G. Fubiani et al., Phys. Rev. ST Accel. Beams 11, 014202 (2008)] was developed in order to provide a three-dimensional characterization of power and current deposition on all parts of the accelerator. The code includes all the relevant physics associated with secondary emission processes and consequently may be used as a tool for design improvement. In this paper, the two accelerator designs considered for the International Thermonuclear Experimental Reactor, that is, the multiaperture-multigrid and the single gap single aperture (SINGAP) designs, are discussed and their predicted performances compared. Simulations have been compared with measurements on prototype accelerators of the SINGAP type. Reasonable agreement between EAMCC calculations and measurements of backstreaming ions and transmitted electrons was found.