The blue circle indicates margin of error. I often see my location on the map as one neighborhood over, but the blue circle just barely encloses my actual location!
I have found that the GPS doesn't work as well for me if I turn it on and off to try to conserve battery power. I have begun leaving it on all the time. I also do not use the wi-fi signal as a means of determining location. When that option is also checked in my settings, it seems to cause the blue circle to grow.
Finally, when you compare the two phones side-by side, where were the two of them in the previous half hour or so? My GPS seems to have a harder time pinpointing my actual location if I've been indoors for an extended time, or if I have been moving around since my last GPS-necessary app was last used.