In different episodes of Friendship is Magic we have seen plenty of Princess Celestia and Princess Luna to understand that they are both equal when it comes to how powerful they are, they both have a lot of magical powers, they both are ancient alicorns and they can both move celestial bodies at will. However, most fans of the show would say that, of the two, they like Pirncess Luna more than Princess Celestia. Let's analyze why with this three points:
1. The Superman Dilemma.
Anyone ever read The Illiad? If you didn't then it's almost entirely about Achilles being really, really angry and killing a lot of people. The son of a goddess and destined for glory, Homer won't shut up about how awesome Achilles is and how he has no equal. Achilles is, in all respects, a superhero before superheroes existed. But unless you're a person that enjoys every single little detail of every work of literature, you probably don't remember that there's one other Greek warrior who consistently and quietly proves throughout the entire epic poem to be just as great if not greater than Achilles. His name is Diomedes, and understanding why he's so forgettable is crucial to understanding why fans don't really care about Princess Celestia.
Diomedes is essentially Achilles without the existential crisis. He is younger, smarter, and more consistent. He defeats everyone he faces, and when he runs out of Trojans to kill because the war is over, he starts fighting and injuring gods instead. Not even Achilles can make that claim, because he dies right at the end of the Trojan war. When talking about Diomedes, the Trojans say, "He fights with fury and fills men's souls with panic. I hold him mightiest of them all; we did not fear even their great champion Achilles, son of a goddess though he be, as we do this man: His rage is beyond all bounds."
And while you may have never heard of him before now, you can still see the Diomedes archetype pop up again and again in pop culture: Legolas in The Lord of the Rings, Snake Eyes in G.I. Joe, and especially Superman in the DC universe. And of course, Princess Celestia in My Little Pony. They are the people (and pony) who are reliable, morally uncomplicated, and generally superior to all the other characters. While we love them, we will never be willing to watch an entire movie, an entire comic book, or an entire TV show made about them and only them.
Why? Because those characters are pillars of solidarity, they are ideals, but unfortunately they have nowhere left to go. For an audience, at least an adult audience, we want the central character to change for the better by the end of a story. We want someone who is deeply broken, who is struggling to keep himself or herself together in the face of adversity, and most importantly, we want a character who isn't invincible. We love Princess Luna and Batman because they are driven by complicated, selfish emotions like guilt and revenge to do extraordinary things under the constant looming threat of them being less than perfect. Superman is what each of those characters would look like divorced of any such threat or ugly motivation. Is it still heroism to leap into a burning building when you know it can't hurt you? That is the Superman Dillema. True with Diomedes in ancient Greece, and true now.
We aren't nearly as interested in acts of heroism as we are in the madness it takes for vulnerable people, or pony, to become heroes. The only way to fit Princess Celestia into that mold is to strip away some of her perfect traits, but the problem with that is ...
2. Princess Celestia stops being Princess Celestia as soon as she slips up.
The moment Princess Celestia is no longer a paragon of absolute virtue and wisdom, it negates everything she stands for as a character.
Quick, what are Princess Celestia's special abilities? Flight, magic, solar power (we suppose), moving the sun around, but what about the intangible power she possesses? Arguably the biggest part of what makes Princess Celestia Princess Celestia is that she maintains an incorruptible moral fiber and an urge to help and guide ponies despite her overwhelming superiority over all of them. Like standing on top of an ant hill while they all bite you and each other, Princess Celestia has the patience to try to help them every day. It is the one thing separating her from other super powerful characters like Princess Luna or Discord: Given the potential to control the world, Princess Celestia never succumbs to ego, or entitlement, or even objective detachment, because she has a sort of super humility. Despite everything she's seen (and being over 1000 years old, she must have seen some really heavy stuff), she stays compassionate towards mortal, non-alicorn ponies, but that compassion only means something as long as she possesses the power to destroy everyone on a whim if she felt like it.
The moment Princess Celestia starts being a jerk that power of character that makes Princess Celestia a symbol of greatness is suddenly gone. A story writer forcing her to falter is actually ruining the best part of who Princess Celestia is. And the worst part is that she not only has power in the form of her being an Alicorn, she also has power in the form of her being a Princess. Which brings us to the third point...
3. She must never have a defect.
I mentioned Superman before because he is basically a character that shares a lot of traits with Princess Celestia, but even Superman has an interesting side: Is he doing the right thing? Can he solve every problem?
Superman has super powers, but a man who can travel faster than a speeding bullet still can't be everywhere at once, which suggests that somewhere there are people dying in warehouse explosions and mass murders and roofing accidents every single day because he's busy stopping a giant meteor from hitting Earth or fighting Lex Luthor. For every person he saves, there are hundreds more, some of them children, taking their last breath while staring hopefully at empty skies waiting for Superman to show up. Superman can't help but set a precedent he can never live up to. From the first time he stopped a bridge from collapsing or diverted a tornado from a town, he instilled a false hope among people: That Superman will save them. That means that every day, even if he never bothered to put on glasses and go to work again at The Daily Planet, Superman is still letting down hundreds if not thousands of people. Add on top of that everyone who is dying of societal problems that are beyond his capacity to fix: homelessness, diseases, hunger...
There's no way Superman can stop homelessness, disease, teen suicide, or domestic abuse. How could he? One of his powers isn't lobbying local politicians. He holds no political power. He can't give homeless people a home.
Princess Celestia rules Equestria, she can totally do that. In fact she did, when she gave land to the Apple family and they settled and started making Zap Apple Jam and helped found Ponyville in the process. She runs the place. If there is hunger, she can divert state funds to plant more crops and provide food to the hungry. If there is disease she can divert state funds to build more hospitals. If there is homelessness she can grant state owned land to build more houses.
There is no problem Princess Celestia cannot resolve if she wanted to. She has all the magical power she needs, all the political power she needs, and all the time she needs (because she's immortal) to solve every single problem of every single pony living in Equestria, all the time. And she does.
Princess Luna couldn't handle that, she wanted more attention and turned into Nightmare Moon. Now she's back, she understands her mistakes, and tries to make amends all the time of her past actions. Discord was a villain, he has so much magic that he can do whatever he wants, he eventually realized that there are more important things in life and reformed with the help of Fluttershy, and now is starting to learn what it actually means to be a good friend and a good character.
Princess Celestia needs to be free of defects, because the moment she starts having one, then she simply becomes like Princess Luna or Discord. Princess Celestia is what characters that also have all the power of magic, and immortality, aspire to be like. She is a role model, and cannot stop being one, because when she does the whole thing falls apart.
Princess Luna doesn't have that kind of "pressue". She has the same power of Celestia, both magical and political, but she is struggling to become good, to improve herself, to be like her sister. She has a road to travel, and we like seeing her traveling it, we relate to that. Princess Celestia is already at the end of that road, she has no more growth to have.
By design, Luna is relatable and therefore more likable. And by design, Celestia is unrelatable, and therefore less likable.