Those "many" were clueless to begin with - IIRC, Sony themselves said when PS4 was revelad (in post conference show with Geoff Keighley) that it's around 10x PS3.
Depends on what metric you use. In some instance the improvement is 17x, some other metrics it is 10x, other metrics it is 8x... But those are all just hard numbers.
They don't tell us the efficiency gains, they don't tell us the new tricks the hardware is capable of.
I wouldn't be surprised if the real-world gain is about 15x once everything is accounted for.
The Geforce in the Playstation 3 was pretty archaic, hot, slow and inefficient.
True that. I don't really recall who was it (it was really long ago), but it was someone from Sony in that interview that said 10x. Which is quite decent.
I can see why most people thought it's not such a leap, always comparing PS2 to PS3 (instead of original Xbox as most poweful console of that gen to PS360), especially after such a long cycle, but it still was quite a nice jump.