Regarding consoles its obvious, it was when PS2 was changed for ps3. But what about PC, when was that time point when new gen hardware came?
The "old" ones were AGP, and new GPUs were starting to max out its bandwidth. AGP was phased out after Pentium-4s and Socket 754 Athlons, and PCI Express became the "new" standard for graphics cards.
The speed of the transition from AGP to PCIExpress was breathtaking. It happened within the space of a year-- Within 2 product cycles (the 6- and 7-series) nVidia dropped all AGP support and went purely PCIExpress. That happened between 2005-2006.