Big cities have many more people concentrated in a relatively small area. This much greater population density means a much greater threat that city folks will have to deal with crime, violence, looting, and riots, especially after the infrastructure starts to break down after any long-term (or even short-term) grid-down situation. Pollution and sanitation will typically be bigger issues, as will the potential spread of disease. Resources such as food, water, and gasoline will quickly be depleted by the sheer numbers of people using those resources. These facts suggest that urban survival needs to place particular emphasis on sanitation and disease prevention/treatment, security and self-dense, and stockpiling/caching supplies likely to run out quickly post-SHTF.
On the other hand, being around more people can have its advantages. More people can mean more hands-on-deck in an emergency, as well as safety-in-numbers. More people probably means more available skill sets. More people may mean a greater opportunity to find and build relationships with like-minded people.
In order to turn these possibilities into reality, urban survival requires you to build community now, before any SHTF crisis. Learn to get along and work with other people, particularly those with different backgrounds from yours. Befriend your neighbors. Get to know them, their attitudes and beliefs, and their skills. Form a neighborhood watch. This can official (working with your local police, posting signs, etc.) or informal (exchanging phone numbers and agreeing to keep an eye out for strangers or anything else suspicious in the neighborhood). The point is you and your neighbors will begin getting to know one another and watching out for each other. You can build from there. Perhaps you will even find some nearby good friends with which you can form a survival group or mutual aid group (MAG).
I've written a number of articles on building community that might interest you. They are listed at the bottom of this article.
Limited space, both outdoor and indoor, is a major obstacle for urban preppers. Most apartment and condo dwellers have no space for gardening, raising chickens, or other homesteading activities (thus their frustration with a lot of typical prepper advice). Even home owners in the city typically have very small yards without much room for those type activities. Additionally, limited storage space inside apartments and condos creates a real limitation on how much food, water, gear, and other stuff you can store.
However, it is possible to overcame these space limitations. My suggestions for doing so can be summed up in three words - minimalism, prioritization, and creativity.
Minimalism - The minimalist lifestyle is about eliminating the unnecessary and superfluous, and doing more with less. This will ultimately free up both space and time (and probably money). Declutter you life. Hold a garage sale. Sell it on eBay. Donate stuff to the Salvation Army. Fill up the dumpster. Doing so will free up an amazing amount of storage space. But where to start? There are lots of articles on the web that you can look up, but here are some of the best suggestions I've seen:
Prioritization - This is crucial for the urban prepper and survivalist. You can't afford to waste space or money on non-essentials. Figure out what is really important and focus your time, efforts, and money on those things. Make lists based on those priorities and stick to those lists. This will also help you in your minimization activities. Once you figure out what is important, get rid of the rest. Prioritized lists will also help you avoid impulse buying, saving you both space and money.
Creativity - Do container gardening on your porch or balcony. Find out if there are any community gardens in your area you can join. See if your church could start a community garden. Store stuff under the bed. Put your bed on risers to create more storage space. Use flat storage boxes to store stuff under the sofa. Create overhead storage areas. Use water bricks to store water, dry foods (beans, rice, pasta, dog food), or even small supplies (batteries, first aid supplies, ammo, etc.). They are made to stack easily, and can even be turned into tables, nightstands, and other pieces of furniture (thereby serving a dual purpose). Another possibility is to rent a nearby storage unit. A final suggestion, watch little house videos on You Tube. They have come up with some amazingly creative ways to use space and create storage.