Grand canonical ensemble Monte Carlo (GCEMC) molecular simulations of hydrogen storage at 298 and 77 Kin triangular arrays of single wall carbon nanotubes (SWCNT) and in slit pores (modeling activated carbons) were performed. At 298 K the US DOE target gravimetric hydrogen storage capacity (6.5 wt %) is reached at 160 bar for optimally configured arrays of open SWCNT of wide diameter, but the equivalent volumetric capacity is similar to 40% of the DOE target [695 (STP)v/v]. For slit pores at 298 K the optimal volumetric capacity is similar to 20% of the target. Simulations for 77 K and 70 bar indicate that triangular arrays of open and closed SWCNT of various diameters in a wide range of configurations exceed the DOE gravimetric target. A capacity of 33 wt % is found for arrays of narrow, open, or closed SWCNT that are widely spaced. Here, adsorption occurs entirely in the interstitial space between the nanotubes. Volumetric capacities close to the DOE target are found for arrays of narrow, open or closed SWCNT with a range of interstitial spacings. The maximum volumetric capacities for simulations with slit pores at 77 K and 70 bar are similar to 73% of the DOE target for a range of pore widths. Capacities from simulations for nanotubes and slit pores at 298 and 77 K are in reasonable agreement with experimentally measured capacities. It is concluded that the potential of carbon nanotubes for storage of hydrogen is superior to that of activated carbons.