We need both to be better designed.
I live in what I suppose you could call a better-designed suburb (or small city; it's all semantics). My suburb of DC has a dense downtown with metro rail and bus access. It has plenty of walkability and apartments/condos for people who want that. It also has townhouses and single-family homes within walking distance of downtown. As you get further from the downtown, it becomes more and more traditionally suburban.
The core issue with this is cost. There are so few places like this in the U.S. that it's expensive to live here. Retrofitting a lot of suburbs with more of a core would help a lot.
The other big issue is what is called missing middle housing. There is a lot of apartments/condos and single-family housing. There aren't many townhouses or duplexes. This creates a situation where many people are either buying more house than they need or living in a space smaller than their needs/desires. This also causes single-family housing prices to be higher than they should be.
Ultimately, retrofitting the suburbs is the great challenge of the 21st century. We need more walkability and density in their cores. Basically, we need to bring back streetcar suburbs (which is what my town is, and after going through decades of losing density, it has been transformed).
And then cities need to become better designed for more people, especially people with families and retirees.