With the original Playstation, Sony was up against a Sega who was imploding and a Nintendo who were hard to work with. It wasn't a lay-down misère, but it might've been. SCEI was in many ways the opposite of Nintento and developers loved it.
The PS2 was up against the newcomer Microsoft. Sony nearly stumbled a few times because Sony Corporate, having let SCEI create this big success with the PSX, could not resist putting their fingers in the mix this time. I suspect knowing that MS were copying with the Xbox what Sony did with the PSX probably saved them as they knew the playbook.
The PS3 and the Xbox 360 were simply More Of The Same. With Nintendo going out of step and then trying to change the rules with their innovative controller, MS and Sony had a partial duopoly. They might've both been in a lot more trouble if Nintento had released the Wii at roughy the same time as the PS3 and Xbox 360. They would've definitely been in trouble if Nintendo had gone for HD and the next-gen graphics instead of just a mild upgrade.
The PS4 and the XBone are mostly a great big upgrade from their predecessors. I've seen game footage of the PS4 and the graphics engine is quite a lot better than the PS3 and the PS3 is pretty good. Plus MS stumbled badly with the "always on" thing and the Kinect. Sony knew better. That will help their reputation quite a lot.
Wade.