I just can't see the jump in graphics which I saw in Battlefield 4 and Killzone Shadowfall. This game looks like a last gen game, barely any difference. I will say the water is great, but they are so much jaggies. The whole masts of every ship are so jagged. And you climb up the top of the city you see jaggies all over it. Is that because the games is one of the first of this gen. Are they going to improve the AA in games ahead or just stuff like the water, which is very cool, but AA for me is more important.

Well Cross-gen games usually have last gen graphics with better resolution/framerate/AA on next gen systems(maybe BF4 is an exception though?).

How better is AC4 on PC?

This is of the only games available for PS4 that I have not bought. It just looks like a really crap effort, and I was turned away from the series after being very disappointed with 1 and 2.

I think future games from UBI will be much better. The Division shows a lot of promise from what was shown so far.

Actually the water and weather effects are vastly better. Though thats about it... Texture do seem a little better.

HBAO Lighting is available which  is marginally better, less jaggies due to more AA available, and camp fires and cannon smoke look better due to physx.  The performance hit is huge for those marginal upgrades (besides AA) 

I aint seen the PS4 version of ac4 with my own eyes. I think its safe to assume cross gen games wont be the star lights.

I think you cracked the question in your own op.

I think it looks great. Remember, its an open world game and not a linear FPS. Cross gen too.

AC built specifically for next gen will look glorious.

Ubisoft addressed this by saying that it is still on an old gen engine but that the next AC will be a real next gen experience.

Cross gen, open world game. 360 and PS3 ports have to die before developers will focus on getting every last drop out of the new consoles.

Battlefield 4 basically is an exception, the game engine (frostbite) was built with high-end PC's in mind which is already capable of pushing better-than-next-gen, hence why there was such a large discrepancy with Battlefield 3 on last generation consoles and the PC.
Just so happens, it translates well over to the new generation of consoles. (Albeit, only high-settings, rather than ultra.)

Assassins creed however is like Call of Duty, they don't push any graphical barriers so they can push out a new game in a short development cycle, thus there is generally very little game engine improvements with each iteration.

Basically, just blame the Xbox 360 and Playstation 3 for holding things back, us PC gamers have been doing it for years now. :P

Basically the graphics could have been better, but Ubisoft doesn't beleive it warrants the cost or development time yet whilst the market is in transition, EA/Dice thought otherwise.