sidewalk edging near city tree

[yardworkswi]

I am a little new to doing edging and have an issue with some of the sidewalks in the "old" part of town. Some of these have not been edged for many years if ever. The issue is when I have a city tree in between the sidewalk and curb which has ground mounded up. When I edge I end up with a small cliff from the turf down to the sidewalk. Is there a better way? I cant think of anything other than leaving it as is. Also do you normally just edge walks and driveway or do you go along the curb/gutter as well. Have seen it done both ways and am up in the air on which way looks better, what do you think or more importantly what do customers expect? Thanks for all advice.