My suggestion, since you're planning to stay on Hatteras, is to look up some maps with distances marked from one side of the island to the other. *Most* of Hatteras island is very narrow! In some parts, you may only be talking about a difference of 40 or 50 feet from the sound to the ocean! I know there is more than one rental house there with unobstructed views of both the sound and ocean!
That said, it's not going to make a ton of difference which side you stay on when it comes to wind. It's always windy here on the OBX. A slight difference has been noted, and I agree with that. But usually March still has just a bit of that winter nip in the air. You're likely to need at least a sweatshirt a lot of the time, either place.
I think NOAA's or the different weather channels' websites have charts of average temps here by month by town, should you want to check those out.
Wherever you land, have a fantastic time! :) And welcome (or welcome back)!