A good rule of thumb for most of Chicago is that higher density living is closer to the lake and it gets less dense as you move further west.
All the best,
But hey...that's not all. Lincoln Park has some of Chicago's best preserved housing stock whereas Near North, a term, incidentally, that nobody in Chicago uses, is mostly saturated with charmless apartment buildings occasionally highlighted by the historic building that somehow escaped the bulldozer. But if you live in the infamous Near North, you have the ability to walk to fantastic stores like Bloomingdales and Neiman Marcus and Apple and so many of those wonderful retailers. And in Lincoln Park, you are stuck with a bunch of smaller independently owned boutiques and local restaurants, which might not be appealing to somebody craving a a Bloomies sale and a bite at the Weber Grill.