It looks like PS4 can handle the APEX destruction demo or something similar in a lot of settings. Such as the Chateau in Uncharted 3. The size of the setting in that scene could really make use of dynamic destruction. I'm sure any close quarters shooter would be great with this and a shotgun or a machine gun ripping through walls in an office building. A lot of potential.

Everything can improve, it just depends on how much developers and publishers are willing to invest into developing those technologies. Half-Life 1 AI's is much more advanced than many modern games, and why? Development costs. Processing power helps, but money is what really matters in the end.

who cares about destruction? What about animations? Imagine how the next Uncharted will look!

Most games this gen cost 2x the amount that Half Life 1 did. 

Money that certainly wasn't invested in AI...

I really want games to be more life like, not in graphics, but in physics, destructible enviroments, and better AI and NPC interaction

Depends on the developer
The Last of Us on the PS3 has the best AI in Gaming as it looks like.
But that is Naughty Dog - The best developer of this Gen for the best console of this Gen.
And they always put 200% effort in their games cause they don't want to make copy+paste standard like many others did in this Gen.
They want to improve with everything they do cause they are never happy.

@Thread
Improvements?
Particles,effects and all that stuff are going to increase a lot.

This is why I don't understand people who say that "we have come far enough, we don't need anything better than this". We have such a tremendously long way to go on animations, physics and the big bad wolf today; AI. A lot of modern games have good visuals but shitty AI and stupid physics and animations often clash with the overall realistic style of a lot of games (and also some of the more stylized games such as Dishonored).
There is so much left to do, on the top of my list is improved AI, this is the area with the biggest room for improvement, developers make use of cheap tricks and scripted nonsense and QTE's to add diffuculty instead of truly challenging AI.

How would you know? 

Exhibit A would be the absolute shit AI in most games today. The only games with a challenge through AI actually being clever are mostly strategy games, turn-based strategy is a lot easier to develop a decent AI for than real time rendered games of any genre.

AI really is the bottleneck for immersion to truly take place in modern games, there really is no doubt about that.