A comparative study was conducted on composite materials having various nanocarbon fillers of different dimensionalities, namely, 1D carbon nanotubes (CNTs), 2D graphite nanoplates (GNPs), and 3D graphite. Comprehensive mechanical, electrical and rheological studies illustrated the complexity of selecting the optimal nanocarbon filler. We found that the mechanical performance of the composite is optimal near the percolation threshold concentration of the filler for all the nanocarbons. The 1D CNTs strongly affected the electrical conductivity and reinforcement of the composite, yielding a narrow range of optimal performance at the lowest filler concentration (0.15 wt%), albeit at the cost of high viscosity. The 2D GNPs demonstrated a wider range of reinforcement with a milder influence on the viscosity at a moderate GNP concentration (3.5 wt%). The 3D graphite filler exhibited similar behavior to that of GNPs, although at a much higher concentration (25 wt%). We introduced a robustness factor as a measure of the filler concentration range at which a valuable reinforcing effect is achieved; this factor increases with the filler dimensionality. These contradicting dimensionality effects are condensed into a figure of merit that takes into account the rheological effect, the mechanical enhancement, and the filler concentration and robustness.