We present a quantitative study of the X-ray morphology of galaxy clusters, as a function of their detection method and redshift. We analyze two separate samples of galaxy clusters: a sample of 36 clusters at selected in the X-ray with the ROSAT PSPC 400 deg2 survey, and a sample of 90 clusters at selected via the Sunyaev-Zel'dovich (SZ) effect with the South Pole Telescope. Clusters from both samples have similar-quality Chandra observations, which allow us to quantify their X-ray morphologies via two distinct methods: centroid shifts (w) and photon asymmetry ( ). The latter technique provides nearly unbiased morphology estimates for clusters spanning a broad range of redshift and data quality. We further compare the X-ray morphologies of X-ray- and SZ-selected clusters with those of simulated clusters. We do not find a statistically significant difference in the measured X-ray morphology of X-ray and SZ-selected clusters over the redshift range probed by these samples, suggesting that the two are probing similar populations of clusters. We find that the X-ray morphologies of simulated clusters are statistically indistinguishable from those of X-ray- or SZ-selected clusters, implying that the most important physics for dictating the large-scale gas morphology (outside of the core) is well-approximated in these simulations. Finally, we find no statistically significant redshift evolution in the X-ray morphology (both for observed and simulated clusters), over the range of to , seemingly in contradiction with the redshift-dependent halo merger rate predicted by simulations.