For the first time we compare two kinds of optical frequency combs, one of which is based on a Ti:sapphire femtosecond laser and the other is based on a mode-locked erbium-doped fiber laser. The comparison is performed by measuring an optical frequency standard with these two combs simultaneously. The two frequency measurements agree within 1.8 Hz ($3.8{ imes}10^{-15}$) with the uncertainty of 17.2 Hz ($3.6{ imes}10^{-14}$), from which it can be concluded that the Ti:sapphire-based frequency comb and the fiber-based frequency comb have no systematic discrepancy at this level of uncertainty.