We study quench dynamics in an interacting spin chain with a quasi-periodic on-site field, known as the interacting Aubry-André model of many-body localization. Using the time-dependent variational principle, we assess the late-time behavior for chains up to L = 50. We find that the choice of periodicity Φ of the quasi-periodic field influences the dynamics. For Φ = ( √ 5 − 1)/2 (the inverse golden ratio) and interaction ∆ = 1, the model most frequently considered in the literature, we obtain the critical disorder Wc = 4.8 ± 0.5 in units where the non-interacting transition is at W = 2. At the same time, for periodicity Φ = √ 2/2 we obtain a considerably higher critical value, Wc = 7.8 ± 0.5. Finite-size effects on the critical disorder Wc are much weaker than in the purely random case. This supports the enhancement of Wc in the case of a purely random potential by rare "ergodic spots," which do not occur in the quasi-periodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law. arXiv:1901.06971v5 [cond-mat.dis-nn]