Wow, you guys are all wrong.The PS4's gpu has 34% more performance the the Nextbox's, That's pretty major, that and the PS4 will have more VRAM for games than the Nextbox if the rumors were true, so it'd be like comparing a Dreamcast's graphics to a PS2's, the difference will be noticeable.

I think when it comes to third party games, we won't see much of a difference. Similar with what we are seeing with third party game this current gen. But if there is a very noticeable difference it will most likely come from first party games and exclusives. The current gen we all saw a major difference between the ps3 and 360 when it comes to First party. For next gen it will be up to te developers to really optimize the console to utilize it at its full potential. 

PS360=Dreamcast
WiiU=PS2
NextBox=Gamecube
PS4=Xbox

I have no idea, does this seem accurate?

qft

No difference at all

According to rumors PS4 is more powerful but we don't know how the system-performance will actually be. The problem is that many just compare the raw numbers but this is not reflecting the actual *system* performance where all parts have to work together.
I think most 3rd-party-games will look almost identical on both consoles. 1st party will be a different story, of course.

If > is 50% more, then according to current speculations it's something like this:

PS4>NextBox>>>>>>>>>WiiU>PS360

For PS4 and NextBox comparison (if rumours are true), this should probably be good comparison

http://www.anandtech.com/bench/Product/549?vs=536

It means that either some options on NextBox versions will be toned down or if all options are same as PS4 version, it will run at lower resolution to achieve same frame rate.

Both are going to be very good looking.  The difference will be significantly less than the difference between DirectX 10 and 11 in this demo (sorry for the bad music): http://www.youtube.com/watch?v=YiS6kzXQch

You have to get more than a 50% difference to make it visually noticeable (think PS2 to Xbox.) So with the current stats that have the NextBox about 30% less than the PS4 it wouldn't really be all that noticeable. I would think it would be a little more than the 360/PS3 differences.

Assuming the Xbox is less powerful, it could be even less as DirectX (Xbox) has become arguably powerful than OpenGL (PS4/WiiU) since DirectX 9. Look at how good Halo 4 looked, and remember it's hardware was mostly designed in 2004. Microsoft has refined DirectX 11.x with the next gen hardware in mind AND there will not be a new DirectX 12 until Windows 9 – so the NextBox/PC games will be even more similar.

Now, I would not be surprised if the hardware is a bit more powerful than the rumors. PS4 is still only 70% of what Tim Sweeney wanted. So if MS kicks up the next box GPU to the 2.5 Tflops he wants, it would mostly be bragging rights, probably not dramatically noticeable.

Actually, here is probably a better demo - directly comparing OpenGL to DirectX.

http://youtu.be/HC3JGG6xHN8

Unless I missed something... the only big difference was ram types.

Consoles went from being ram starved last gen to having... if anything, a little to much ram to the point of where you wonder what non next gen overlays and apps they're going to try and push.

Which means, if your looking for a difference in terms of graphical looks... you are probably going to be disapointed.

What you should be looking for is a differnce in "complexity".

To put in in RPG terms.   Instead of 8 Kobolds vs 8 Orcs.

Expect 8 Orcs vs 10 Orcs.   The orcs probably won't look any better... but the PS3 will be able to put more of them out.  So PS4 worlds will look the same, but will put out more realistic "alive" worlds.  (In the few exlusive games that use them) and are less likely to have framerate issues and pop ins by quite a bit.