The weird PS1/PS2/PS3 were because of Japan's heavy arcade culture, where quirky hardware/software designs were the standard. Xbox was approached from the "let's make a DirectX Box" angle, from commodity PC hardware, and it wasn't until the PS3's initial huge cost blunder that Sony realized they needed to go the commodity angle.

> There's a persistent rumor that the Cell was so powerful that Sony had intended for the Playstation 3 to be equipped with two Cell chips, and no true GPU at all. But it seems Sony realized during development that their philosophy had no future.

The original plan was for no GPU at all, relying on the SPUs as pixel processor units. When they realized that that wasn't feasible for a few reasons, they quickly partnered with Toshiba to make a custom GPU, and that ended poorly too, so Toshiba scrambled and licensed an NVIDIA core. The final "RSX" chip was still a Toshiba design, but with NVIDIA at the center.

As games got more and more complicated, the amount of developer support & tooling did as well. The Xbox 360 had incredibly strong tooling (ask someone who worked on the device about 360's PIX, and they'll gush for days), and the PS3 had very little. The PS3 shader compiler infamously had a random search for an optimizer, and Sony's recommendation was to just run it continually with different random seed inputs in hopes it found a better optimization for your shader.