The SNES lasted a while in the market, and—almost uniquely among consoles—it ramped up in power
over its lifetime by putting coprocessors like the SuperFX into game carts. By the end of its lifetime, the "system" of the SNES + a cart like Starfox, was much closer to the N64 than the base SNES, making the N64 much less of a shift than it seemed.
Interestingly, if you think of the PSX as descending from the SNES architecturally, it's nearly identical to the end-state of "SNES + SuperFX GSU-1", but with the one added feature of DMA-streamed block IO from the CD device. (Thus why the FF7 demo on the N64 used polygonal backgrounds, while on the PSX you get pre-rendered backgrounds. Each version plays to its console's strength. Makes you wonder what would have been possible in an alternate world where the N64 had a CD drive as well as its better polygon-pushing abilities.)
This also means that the PSX->PS2 likely represents the largest single-generation leap in power of any console: it was a catch-up from "basically a SNES" to modern-for-the-time hardware, representing a literal 10x jump in CPU and GPU power.