Having done both, I can tell you they are very different lifestyles. There are certainly perks to the downtown lifestyle, but it isn't all peaches and roses.
Taking the bus is a huge mixed bag and depends a lot on the transit system layout. Taking a newborn on the subway and transferring to a bus to see a pediatrician sucks. Hyperactive kids fighting all day when you're trying to work from home from a shoebox apartment sucks. You don't get as much leeway in your choice of schools (and btw, the highest ranking ones often aren't downtown). Etc.
By contrast, the north american suburb lifestyle generally involves driving kids around pretty much all the time: they might go to a nicer school that is a bit farther out (did I mention good school areas have expensive real estate?) One might drive out virtually every weekend because getting ice cream at ikea takes as long as it does to walk/bus to the nearby supermarket. When one drives, they can also pack more activities in one day: Going for groceries then checking out a dozen books from the library in a single outing isn't a recipe for back pain. And you can actually get home before lunch time. Etc.
With a bigger house, your parents can come stay for a few months (this is very common in many cultures).
Yes, you can save money by living the downtown lifestyle, but there's certainly a hit in various aspects of quality of life.