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I'm just getting the hang of taking pictures of my city at night/dusk, and I'm bracketing exposures to get deep colors for the sky and enough exposure for the buildings. Here's an example. I've put the original dark and light exposures below.
Basically, the illuminated names on the tops of buildings lack the clarity of the underexposed image. Is there a way to get around this, either when taking the original high exposure photo, or in post-processing?
They're being blurred out by camera motion as much as they are by being overexposed. The obvious solution is to use a sturdy tripod. Good tripod technique for such long exposures includes a way to release the shutter without touching the camera. For shutter times between about 1/100 second to 1 second mirror lockup, if your camera has a mirror, will also help to reduce blur caused by vibrations resulting from mirror movement.
When using a sturdy tripod and exercising proper technique, there should not be any perceivable difference in the framing of the scene from one shot to the next.
Depending on exactly how you are combining the two images, you can also bring down the highlights in the brighter exposure before combining them.
You need to use a tripod to eliminate motion blur as Michael Clark also points out. Also the exposure time to get the light sources correctly exposed is very short. I've taken night shots where I was exposing for 40 seconds at an ISO of 1600 to get the background correctly exposed, while I was exposing for 1/400 of a second at ISO of 100 to get the city lights correctly exposed. In that last exposure the entire picture looks pitch dark, only if you zoom in at the right places will you see illuminated pixels that happen to fall right on bright lights, nothing else is visible in that picture.
You then need to take quite a few intermediary exposures to allow the software to chip away the extremely blown out highlights of the long exposure and replace that with information present in the shorter exposures.
The basic problem is one of large dynamic range. The range is higher than normal daylight shots because the light sources are in the picture, and you want to resolve their details.
You therefore address this as any other large dynamic range problem. The first approach is to expose so that the part of the highlights you care about end up just at the end of your sensor range. The dark parts then fall out where they fall out. With a good sensor, there can be enough dynamic range captured that this is all you have to do.
If you're not wasting range above the bright spot and there is still too much noise in the dark areas, then things get more complicated. HDR (high dynamic range) techniques require taking multiple picture. One puts the highlights at the end of the sensor range as before. Take one or two more, each 2 f-stops more exposed. The highlights will clip in those, but more detail will be captured in the dark areas. Clever software then picks the best parts from each frame and makes a composite with good detail in both the highlights and the dark areas.
According to this method, your first image is still overexposed as can be seen here:
The highlights are still blown out. I'm just guessing, but to capture them acceptably you want at least one EV less, probably two.
However, in your case you have another problem, which is camera shake. This is evident everywhere, but is particularly easy to see by looking at the trails left by point light sources:
The solution is to hold the camera more steady and/or use a faster shutter speed. A tripod is a obvious thing to use in this case, since your scene isn't moving and a slow shutter speed would give you other advantages in picking the exposure. It is also necessary if you end up using multiple-image HDR techniques.
The highlights in your second picture look worse than in the first picture because they are more blown out, and just as wobbled:
To see where you're at with using a single image, here is a section of the first picture with non-linear brightening to show detail in the dark areas:
You can see reasonable detail in the dark areas, but splotchiness is starting to be evident. This can be see particularly on the dark smoke stacks. However, this example above is from post-processing your 8 bit image. There should be considerably more dark detail available in the raw image.
Given all the above, it may be possible for you to get what you want from a single shot. Use a tripod, and try 1 EV less exposure than your first picture, then see what is really available in the raw file.
