The Height and Hillcrest (and I'll throw in Stifft Station, the area that surrounded hte old trolley stop leading into Hillcrest, and Capitol View, the area that grew up early in the 20th century and overlooked the state capitol since those two areas really operate as extensions of Hillcrest) are both wonderful areas. I'll admit a preference for Hillcrest because it's a bit more open and retains both its homes and its shops with a....well, neighborhood feel a bit better than the Heights.
My wife and I lived in Hillcrest and then moved west when our second child was born, thinking to save money, and it's a move we've regretted ever since. We plan on going back as soon as possible. Hillcrest, just to speak of my personal favorite of the neighborhoods mentioned, is a jewel and Little Rock hasn't done nearly enough to help preserve it or its other neighborhoods that are older and yet still remarkably stable. For example, unlike Hillcrest/Height/Capitol View/Stifft Station and the more affluent parts of the Quapaw Quarter district, the neighborhoods that grew up in the earlier part of the last century around Central High were wonderful and full of beautiful houses and our city has simply let the area slide.
Little Rock's primary flaw as a city is that we have a city manager government, with some of our directors elected citywide and thus giving west Little Rock the predominant voice in our government. Little Rock is a wonderful place to live and it's my home town, but I look across the river and see what a good mayor/council style government is doing to help preserve and rebuild NLR and I envy them.
