I live in Wilmington, and whichever Beach you choose, Wrightsville or Carolina you will have plenty to do. I t seems to me that Wrightsville Beach is great for hanging on the Beach all day, maybe a little more quiet but not really. More expensive Hotels and restaraunts. All around it feels a little more upscale..
Carolina Beach has a boardwalk, it has an older feel to it, and is scenic in its own way and very laid back. If you choose to stay at Carolina Beach...you MUST eat Britts Doughnuts..enough said!!!!
Carolina Beach is closer to the aquarium and the civil war museum at Fort Fisher. You can also catch a Ferry and go into Southport for sime shopping.
You should come into Wilmington just to go into Downtown Wilmington if nothing else..it is great..lots of good places to shop!