Playstation 3 had a PowerPC 970 in-order CPU, at 3.2 ghz, running the entire game. One 1.6 ghz Atom core is as good as a PowerPC970 in-order CPU for most tasks. In fact - both take up similar transistors sizes, and score the same on zip compression. Thus the Playstation 3 is powered by just a 1.6 ghz Jaguar (similar to Atom) core. This one will have 8. Thus making it at least 8 times more powerful in general purpose programming - on the same code - by this metric alone.
However - the PowerPC 970 for the Playstation 3 also has no branch-prediction - since it has no out-of-order code execution. Thus - the Playstation 4's CPU will be even more then 8 times more powerful at general code. I'm guessing 10 times.
Compare this to Xbox 360 versus Xbox 1. The Xbox 360's CPU, I heard developers say, was only 2-3 times more powerful then the Pentium 3 733 mhz. Thus - a far greater jump this generation in that sense.