We know they both "wear a royal mask"* - Celestia out of duty, Luna to protect her vulnerable (and heavily-damaged by the time spent in exile as "Nightmare Moon") natural personality. We get glimpses behind those masks (particularly in "Best Night Ever" and "Luna Eclipsed"), but we've never see them completely come off (at least on the show itself). That would be something that only occurs behind closed doors, between the two of them alone or with a very select few they have allowed to look behind the mask (Twilight Sparkle, Cadance, probably Shining Armor as well**).
For a show that places so much emphasis on sister-sister relationships (besides Celestia and Luna, there's Applejack and Apple Bloom, Rarity and Sweetie Belle, Rainbow Dash and Scootaloo adoptively and Twilight Sparkle and Cadance as in-laws) there's a LOT we're missing out on.
**As a side note, I tend to think what Shining Armor was "doing" during the time of the first two seasons was spearheading Luna's background rehabilitation. He had already earned Celestia's deep trust from his connections to Twilight and Cadance, his moral character and his employment in the Royal Guard, so he would've been the natural choice for that task.