Let's set some terms right first.
Ambient lighting in CG of all kinds is a constant and directionless source of light that's applied to everything. It is dull and it decreases contrast and flattens the image and all, and it's of course very wrong. Most people aren't using it anymore, as it's a legacy from the early days when even a single additional light source was very expensive. Think eighties CGI.
About 14 years ago ILM introduced the concept of ambient occlusion with image based lighting. The ambient term wasn't just a constant value, it was sampled from a spherical environment map which was usually created from shooting pictures of a chrome ball and unwrapping them into a texture map (as the tech was developed to make movie VFX more realistic and the lighting workflow more simple).
But this has the unwanted effect of illuminating the entire surface of all objects, which isn't realistic. ILM's solution was ambient occlusion, basically precomputing the visibility of the environment for every point on the surface. It's possible to calculate AO as a texture map, or as a pass of an image which then gets used in 2D compositing (similar to how a g-buffer works).
AO however is not a physically correct approach at all, it's a fast and cheap hack. ILM used raytracing but it's also possible to render it with other methods; and it was developed mainly because full raytraced lighting was way too expensive at the time.
Also, AO doesn't calculate lighting, so it can't produce effects like bounce lighting or color bleeding in the bounced light.
Game renderers have different implementations and they also had an intermediate step. I think it was Half-Life 2 where Valve first introduced ambient cube maps for the characters' lighting - this was more advanced then a simple constant ambient term. Not sure why they haven't used a spherical environment map approach though, perhaps it has to do with the math and the GPU features of the time.
Screen space AO techniques are, as I've been mentioning for a while now, an approximation of the VFX tech, less accurate but more efficient. So basically a hack of a hack
I don't think the current console generation is powerful enough for developers to phase it out completely and replace it with a 'proper' bounce lighting system, but we're probably going to see a few additions and such in the coming years.
Area lights are a relatively new thing in CG, as the name suggests the light source is no longer handled as a single point or a general direction. This is also of course much more expensive, and usually requires raytracing; KZ4 is once again using an approximation instead.
Area shadows are however a completely different thing, even though it's possible and common to pair them with area lights and use similar calculations (it's best with raytracing, of course). But they're a lot cheaper and can be implemented for example by simply calculating multiple shadow maps for a light source and then combining them.
As for UC4 and it's issues, there seem to be some camera angle related shader stuff on the characters (and probably any dynamic object) that does not handle shadowing or occlusion or whatever in the object. This was very common in PS360 games but I have seen it less frequently in PS4X1 titles. SSAO should help with the issue theoretically, so maybe it's something ND plans to deal with later on. Or maybe this is one of the trade-offs they're making to get to 60fps.
