One thing that was not discussed in the previous response was the offset one is able to make from mortgage interest against taxes owed. Oftentimes, the interest paid on the first year of a mortgage will result in an offset against your taxes due and thus, create a return. I typically take that return and apply it to the following years house payments. Therefore, once you get going (and provided you are under a certain income level), the cycle will perpetuate itself.
You also accrue equity in owning a house which can then be translated towards your own monetary worth when applying for a loan with a lender. Apartment dwellers do not have this as an option, unless the apartment is a co-op and owned by the tennant.
Finally, as a "renter" (be it in a house or apartment), the tennant does not always have free reign in how they modify the dwelling. Paint colors may be dictated by the owner, as would any structural modifications.
I do, however, understand why many of the well-to-do in the world have both homes and apartments in cities. Apartments in a city are a wonderful alternative to a hotel where one can visit the city, see a show, or attend an event and then depart back to where they "live" to a home.
Just a few of my own thoughts....
I grew up in a New York City apartment until the age of 17. I now live in a home on seven acres of land in a smaller town. I love my home. As fond as I am of the city and I do miss the excitement of being in the midst of the action - I wouldn't trade my house for anything!