GIS Point or discrete longitude and latitude columns?
Points are useful for spatial relationships.  You can determine what points are within polygons (addresses within a city boundary, as a city is rarely a simple square), what point is closest to another point (bakeries near your home), etc.  Using Lat/Long you can calculate some of this but there are times that Lat/Long will get the answer very very wrong (http://workshops.boundlessgeo.com/postgis-intro/geography.html).

A great intro to geometry in Postgres:
http://workshops.boundlessgeo.com/postgis-intro/

Another way of looking at it:
Looking at a map of the United States how would you quickly determine if a point is within the country?  By using min/max lat/long you would have to include AK and HI (and maybe Puerto Rico, Guam, etc) and the min/max box of lat/long suddenly won't work because it overlaps Canada/Mexico/etc.  But using a point you can then check via ST_Within() in a quick geometry check.