We compare the results from a state-of-the-art semianalytic model of galaxy formation with spectrophotometric observations of distant galaxy clusters observed in the range 0.8 ≤ z ≤ 1.3. We investigate the properties of their red sequence (RS) galaxies and compare them with those of the field at the same redshift. In our model we find that (1) a well-defined, narrow RS is obtained already by z ≈ 1.2; this is found to be more populated than the field RS, analogously to what is observed and predicted at z = 0; (2) the predicted U- V rest-frame colors and scatter of the cluster RS at z = 1.2 have average values of 1 and 0.15, respectively, with a cluster-to-cluster variance of ≈0.2 and ≈0.06, respectively. The scatter of the RS of cluster galaxies is ≈5 times smaller than the corresponding field value; (3) when the RS galaxies are considered, the mass growth histories of field and cluster galaxies at z ≈ 1.2 are similar, with 90% of the stellar mass of RS galaxies at z = 1.2 already formed at cosmic times t = 2.5 Gyr, and 50% at t = 1 Gyr; and (4) the predicted distribution of stellar ages of RS galaxies at z = 1.2 peaks at 3.7 Gyr for both cluster and field populations; however, for the latter the distribution is significantly skewed toward lower ages. When compared with observations, the above findings show an overall consistency, although the average value ΔU-V ≈ 0.07 of the observed cluster RS scatter at z ≈ 1.2 is smaller than the corresponding model central value. We discuss the physical origin and the significance of the above results in the framework of cosmological galaxy formation.