The Near North Side is mostly high-rise living. Whereas Lincoln Park is much more of a mix, but definitely lower density. Because the Near North Side is so close to downtown you have much more single occupancy options, but it is more expensive. Lincoln Park is still pretty expensive, but there are a lot of different options for housing. LP also has slightly easier parking to the west. Both are equally great neighborhoods, so it just depends on your lifestyle.
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.