On the structure of the turbulent interstellar atomic hydrogen. II- First comparison between observation and theory

{It is necessary to understand the dynamics of the atomic gas to use complex modeling and to carry out detailed comparisons between theoretical models and observations.}{In a companion paper, we present high resolution bidimensional numerical simulations of the interstellar atomic hydrogen. Here, we further characterize these simulations and we compare our results with various observations.}{We give statistics of the column density and velocity along the line of sight and show that they compare favorably with observations of high-latitude lines of sight. We compute synthetic HI spectra and qualitatively discuss the information that could be inferred if these spectra were observed. Finally, we extract CNM clouds and study their physical properties finding strong similarities with real clouds. In particular, we find that the clouds follow Larson-type relations, i.e. $M \propto L^\gamma$, where $\gamma \simeq 1.7$ (we speculate that in 3D, $\gamma \simeq 2.5$) and $\sqrt{<\delta v^2>} \propto L^{0.4}$. We also find that the distribution, ${\cal N}(N)$, of the column density, $N$, of the CNM structures formed in the simulation follows ${\cal N}(N) \propto N^{-1.2}$ which is marginally compatible with the observational result obtained by Heiles & Troland (2005). From the mass-size relation and the mass spectrum, we derive an exponent for the column density distribution close to the value obtained in the numerical simulation.} {We conclude that the simulations reproduce various observational features reasonably well....}