The best of the PS1 didn't come out 14 months after the 3DO, but 5 or 6 years after the 3DO. It would be more fair to compare 1994-1996 PSX games to 1994-1996 3DO games.
I would say up until 1996 myself.
Jaguar is often said by some developers to be very powerful, close to the PS1, but theories don't work when there's nothing to show for it. If you don't have anything to show this mysterious secret sauce is it's all imagination..
I posted the Jaguars best graphical achievement earlier and I'll post it again here:
You are right that the Jaguar would struggle to replicate Need for Speed. This is the best it can do and no matter what theories the Atari sites come up with, unless I see a game better than this it's all pointless.
This is a Jaguar CD game released late into its life,
Need for Speed on the 3DO was an early 3DO game that looked like this:
It's clear there's a big difference here, the Jaguar was just too weak and badly made.
It's better than the 32X though.