- The sameness. Every house on the streets where I grew up looked virtually identical, as did the neighborhood where I bought my first house. It took owning a house in the 'burbs to remember how much I didn't like the cookie-cutter aspect. Doubly so for the fact that virtually every suburban neighborhood built in the past 20 years has an HOA, which I detest.
- The distance. Going to anything, even just a Wal-Mart to get groceries, meant a minimum of 10 minutes just to get out of the "residential area" and make it to the "commercial area." The one corner store we had was usually under pressure from the city government and nearby residents to close down because of, allegedly, too much traffic.
- Minimal cultural differences. Yes, my hometown had a Western Days Weekend and an Old Town District but that was it. The town where I bought my first house (this was a bad idea, in retrospect) didn't even bother with that. Everything else in both places was strip shopping centers or Wal-Mart or paved six-lane roadways to get people out of town to the big city for work and then back into town to get to sleep at night. Going to do anything, like a zoo or museum or a baseball game, meant a half-hour minimum drive. There are lots of suburbs in north Texas, let's say, that exist solely for zoning authority.
You mentioned being outside and being kids. The city where I live now, Seattle, has a massive parks system. My tiny house on a tiny lot in the city still has about 1,600sqft of outdoor area to play in and a huge tree. Even the apartments we've rented have a courtyard and are near to parks and sidewalks and places to play. It's great for people whose kids are outdoor types; mine prefers to be inside with books and puzzles and computers.
What I like about raising our kid in the city: Exposure to new and different ideas; most cities aren't self-selected to be the same as each other. A varying cityscape that isn't just the same houses feeding to the same street and to the same businesses. More cultural and entertainment options are close at hand. Being able to live in a more environmentally sensitive way (my kid doesn't want to learn how to drive and prefers to take transit and has made compost and recycle separating into a game).