Here we measure the absolute magnitude distributions (H-distribution) of the dynamically excited and quiescent (hot and cold) Kuiper Belt objects (KBOs), and test if they share the same H-distribution as the Jupiter Trojans. From a compilation of all useable ecliptic surveys, we find that the KBO H-distributions are well described by broken power-laws. The cold population has a bright-end slope, $alpha_{textrm{1}}=1.5_{-0.2}^{+0.4}$, and break magnitude, $H_{textrm{B}}=6.9_{-0.2}^{+0.1}$ (r-band). The hot population has a shallower bright-end slope of, $alpha_{textrm{1}}=0.87_{-0.2}^{+0.07}$, and break magnitude $H_{textrm{B}}=7.7_{-0.5}^{+1.0}$. Both populations share similar faint end slopes of $alpha_2sim0.2$. We estimate the masses of the hot and cold populations are $sim0.01$ and $sim3times10^{-4} mbox{ M$_{bigoplus}$}$. The broken power-law fit to the Trojan H-distribution has $alpha_textrm{1}=1.0pm0.2$, $alpha_textrm{2}=0.36pm0.01$, and $H_{textrm{B}}=8.3$. The KS test reveals that the probability that the Trojans and cold KBOs share the same parent H-distribution is less than 1 in 1000. When the bimodal albedo distribution of the hot objects is accounted for, there is no evidence that the H-distributions of the Trojans and hot KBOs differ. Our findings are in agreement with the predictions of the Nice model in terms of both mass and H-distribution of the hot and Trojan populations. Wide field survey data suggest that the brightest few hot objects, with $H_{textrm{r}}lesssim3$, do not fall on the steep power-law slope of fainter hot objects. Under the standard hierarchical model of planetesimal formation, it is difficult to account for the similar break diameters of the hot and cold populations given the low mass of the cold belt.
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