What works in a rural/wilderness area can still be useful in an urban area, but much that you would carry on a business trip in your suitcase will not help much in the woods. In a larger disaster, you may evacuate, but get stuck on the road out. Or the area you go to could lose power, or suffer from an emergency also. You can still use a tent to camp in a friend's back yard, or even an airport (yes I have seen that done). Some of the tools may not be acceptable in some areas, such as axes, machetes, hatchets, large knives; but I still take them (unless flying).

I generally travel with my usual work clothing, suitable for the climate and the work, and I also carry my emergency stuff. For my house, my family has BOBs with field equipment, and a small duffle with more clothing and more urban stuff.

The principles never change, whether in the wilderness or New York City. You need water, shelter, signaling, heat. Yes, the water purification may be unnecessary, but then again it may be needed. Some refugee shelters I have seen were worse than a wilderness environment.