Should there be a difference in strength or otherwise between daytime and nighttime auroras? Or do they have exactly the same characteristics?
I.e. if I observe them in a place where it’s dark 24 hours. 
 A: 
Should there be a difference in strength or otherwise between daytime and nighttime auroras?

The geomagnetic poles are not aligned with the geographic poles, which are already tilted away from north/south ecliptic.  Regardless, the auroral oval is not symmetric between the day and night side of the Earth.  It is generally more extended on the nightside than the dayside (i.e., it goes to lower latitude on the nightside) when North America is on the nightside.  This is because the south geomagnetic pole is within the Canadian Arctic Archipelago.  Thus, it is much easier and more common to see an aurora in the United States than in many parts of Russia.

Or do they have exactly the same characteristics?

You cannot see the aurora with your eyes on the dayside, it is much too faint.  This combined with the stretching of the terrestrial magnetosphere due to the consistent dynamic pressure exerted by the solar wind.  We further have many more observatories in the Western Hemisphere which leads to there being more nightside observations in the Western Hemisphere.
The aurora is most easily seen in ultraviolet, which is why the DE-1, TIMED, and Polar spacecraft had UV imagers to look at the aurora.  The problem is that the dayside of Earth emits a lot in UV as well, so the dayside aurora is difficult (not impossible) to image.
The auroral oval can be nearly circular at times, but this is less common than the distortion toward Canada.
Side Notes
Note that all of the above is with regard to the auroral oval in the northern geographic hemisphere.  The southern geographic aurora is different for several reasons and less well observed (fewer people live at high enough southern latitudes to routinely observe it).
