The instability, dynamics, and morphological transitions of patterns in thin liquid films on physically and chemically heterogeneous patterned surfaces are investigated on the basis of 3D nonlinear simulations. On a chemically striped surface (consisting of alternating less and more wettable stripes) the film breakup is suppressed on some potentially destabilizing nonwettable stripes when their spacing is below a characteristic length scale of instability (lambda(h)), which is of the same order as the spinodal length scale (lambda(l)) of instability on the less wettable stripes. The thin film pattern replicates the substrate surface energy pattern closely only when (a) the periodicity of the substrate pattern lies between lambda(h) and 2lambda(h) and (b) the less wettable stripe width is within a range bounded by a lower critical length, below which no heterogeneous rupture occurs, and an upper transition length, above which complex morphological features bearing little resemblance to the substrate pattern are formed. The thin film pattern on a periodic physically heterogeneous surface shows the loss of ideal templating when the periodicity of the surface is smaller than about 0.8 times the spinodal wavelength evaluated at the minimum film thickness. On a physicochemically patterned periodic surface, the chemical heterogeneity largely controls the thin film pattern and the effect of small to moderate physical heterogeneity is minimal.