There are several differences between urban and wilderness survival.

Darkness is more likely in an urban situation; if you are inside a building and there's a power cut, it's likely to get pitch dark. A lot of places have emergency lighting but I wouldn't rely on it. Where-as outdoors it's rarely truly dark. So carry a decent torch.

In urban environments you are more likely to be trapped inside a collapsed building. Further, the materials you're likely to have to deal with will be artificial: steel, brick, wires etc, and may be held together with screws or nails. This affects the tools you may need. A multitool with screwdrivers etc is good, and a hacksaw blade that can cut metal may be more useful than a woodsaw. I think a prybar, even a small one, can be more valuable in an urban environment than a wilderness one. A tin-opener will get you more food than snares.

There will be people around. This is mostly a good thing: it means you can call for help if you get injured or trapped. Carry a whistle. Also a cell phone: cities generally get good signal which you might not in remote areas. Other people may call on you for help so it's even more important than usual to carry spares. It's better to have two or three small torches than one big one, so you can give the spare ones to other people.

Lots of urban problems can be fixed by money. Carry spare money.

There will be dust. Carry a dust mask. I've read that in 9/11 the most valuable EDC were torch, whistle and dustmask.

There are things you are less likely to need. You probably won't need a signal mirror in a city. Tap water will likely either be pure enough to drink, or polluted by chemicals that a wilderness kit can't cope with. Fire-starting is rarely a problem. Likewise building a shelter when you are surrounded by buildings.