without a doubt from the 5th to the 6th. That's not to say the 6th-7th jump isn't substantial (though I would argue that it was fairly moderate for GC-Wii), but it doesn't compare to the 5th to the 6th.

From a polygonal standpoint, the amount of polygons the PS3 can theorhetically pump out nearly 4 times as many polygons per second as the PS2. The PS2 could pump out over 200 times more polygons per second when compared to the PSX.

From a chipset standpoint, the PS3 and PS2 both use 64-bit chipsets, the PSX used a 32-bit chipset. Oddly enough, The Dreamcast used a 128-bit chipset and is the only console to have done so (Gamecube, Wii, Xbox, Xbox 360, PS2, and PS3 were all 64 bit). While the N64 had a 64-bit processor as well, no developers ever actually took advantage of it, so it is more or less a 64-bit chipset with 32-bit games.

From a technical standpoint, the jump from PSX to PS2 was immensely larger than the jump from PS2 to PS3.

This. Jump from SNES to N64 was huge. It was basically jump from 2D to 3D.

6th to 7th.
It's obvious when you compare MGS4 to the the previous ones on PS2. HUGE JUMP.

That BF3 pic is definitely from the PC version. I doubt they released any PS3 or 360 images.

Out of the two choices offered; 5th to 6th, without a doubt. I've spent to much time gaming to claim otherwise.

That 150 million polygons per second PS2 number was way over inflated by quoting the number of untransformed triangles it could proccess, the actual numbers were 66-80 million static 15–20 million animated (http://www.technology.scee.net/files/presentations/agdc2000/ThePowerOfPS2.pdf) and real world performance of textured and lit polygons has been quoted as 500-650k at 30fps vs the PSone's 360,000 polygons transformed per second and 180,000 texture mapped and light-sourced polygons per second vs the PS3's 270 million transformed and it is also possible to use SPUs to generate aditional geometry so it's not that clear cut plus geyometry on the PS3 is a weak point compaired to the 360s 500 million. And the bit width of CPUs hasn't mattered since the 32-bit era, in fact the Cell actually has a 32-bit instruction format tho it does have some 64 and 128 bit registers, modern CPUs are just not built the same anymore so it's really aplicable to modern CPUs unless you are talking about memory addressing of more than 4GB of RAM.

If we compair the sytems by other metrics the picture is very different if we talk clock speed for example we go from 33Mhz PSone to 299Mhz PS2 3.2Ghz + 6 SPUs which is a far larger leap from PS2 to PS3 than one to 2.  RAM goes 2MB + 1MB video for PSone 32MB unified + 4MB frame buffer for PS2 to 256MB + 256MB video for PS3 which is once again a PS3 win. 

I don't know, hard to say. Both were pretty big but in a different way. 6->7 moved us away from blockyness and towards more natural shapes, while 6->7 really made things beautiful. It also depends greatly on what kind of games we compare. I must say that I personally value open outdoor areas pretty high, and that was pretty rare before this gen. And I'm talking visually as well.