At wide aperture you are depending on the precision of the whole area of the lens. The larger the lens the more difficult it is to configure them to "diffraction limited" specifications. (This means that the lens cannot resolve any more detail than is possible by the physics of light itself.) So there's always a trade-off going on. Larger diameter lenses *can* resolve more detail but *only* if they are ground to absolute precision. This is why DSLR glass invariably produces softer images at wider apertures, just due to their size.
Now you have another thing at play. At wider apertures you have to focus much more precisely. Your DOF is not as forgiving at wider apertures. I suspect that your wide-aperture images might be suffering from mis-focus more than poorly ground lenses. At wide aperture you have to depend on precision focusing and precision ground optics. At smaller apertures you hit the other wall and you delve into the area of diffraction limitations. Wider aperture can provide sharper images if all things are going in your favor. There's always a sweet-spot somewhere in the middle of any lens design where aperture (for resolution and lens quality) benefits more than the diffraction limitations and deep DOF at smaller apertures.
The nice thing about the smaller P&S lenses is that it is much easier to grind them to precision curvatures. So that sweet-spot can span a wide(r) range of f/stops. Whereas in larger lenses for DSLRs there's usually only one f/stop where they get the best images.
Ok. So what you are saying, that the reason the photos at F2.8 were less focused, is because of the shorter DOF (which makes sense), so the camera has big problem to decide what to mis-focus (if some of the lights are near and some are far).
In my photo, i was photographing some street lights along with far city lights at infinity. It now seems, after considering DOF, that the camera had to "average" focus between them, so the far lights seems almost sharply focused, while the near street lights are soft and out of focus.
Now it all makes sense, thanks!

Where can i learn all about photographing and digital photographing in particular?
I'm reading some articles on Wikipedia, but i would like more material to study from.