The animation that PD created in game is to smooth the mesh topology changes over time so it doesn't visually jar (as much). The weirdness you see in photomode is probably because the adaptive process depends on the FoV etc.
PD weren't just "tessellating" (which is a misnomer anyway, call it subdivision), they were also using progressive meshes (alongside now-usual discrete LoD systems). This meant they stored a low-detail mesh, then all the necessary additional vertices, in order, required to gradually add information to that low-detail model, from the full-detail model they made for the game, bit by bit. "Progressive meshes" should be your starting point to understand what we see in some cars in GT6.
The "tessellation" worked on top of that, further subdividing beyond the detail stored in the mesh file, according to certain primitives (e.g. a polygonal approximation of a circle). It's likely that the ultra-low detail of some of these primitives at times in-game was unintended. It's much harder to tune an infinitely variable "LoD" system than it is a discrete one.
The subdivision occurs each frame, and is effectively immediate in both games. The progressive mesh / LoD setup is more involved, topographically speaking, so it makes sense to spread that out over several frames anyway, but it helps with the visual problems, too, as I already mentioned. Both of these processes ran in tandem on the Cell, before the GPU even got a sniff of a vertex. That's very different to how it works on PS4, likely meaning that the progressive mesh aspect has been dropped altogether and we're left with the vanilla tessellation (subdivision) offered by the GPU's dedicated hardware unit.
