What do you think would happen to Equestria if some other pony took over Celestia's position as the ruler of the land?
-Applejack: Understands the value of hard work but not much of other things related to ruling a country. Equestria's scientific development would stagnate and culture would become more about "worker heroes" and monuments to productivity, but the nation would still remain powerful as an industrial giant.
-Rarity: Knows royal etiquette and handles diplomacy well, but tends to favor form over function when it comes to practical matters. Much more spending on public appearance at the cost of efficiency, but would still keep the country running.
-Pinkie Pie: Would celebrate every day and throw big parades, universally loved as the best princess ever. That is, until the nations budget runs dry and the actually serious matters need to be adressed. Pinkie tries to sing a "lets fix the nation" song, but Pinkies songs don't tend to work when they're painfully forced so she would get overthrown and Equestria would probably become a democracy instead.
-Rainbow Dash: Would expand Wonderbolts exponentially while handling other matters half-assedly. Eventually Princess would become to mean just the commander of airforce, while her assistants would do the actual ruling of the country on her behalf.
-Fluttershy: Would be very kind and thoughtful about every decision, although stressing a lot about the hard decisions. After compromising too much in several meetings, her friends would arrange her a council to help with the foreign affairs. Princess Fluttershy would continue as the leader of domestic affairs, while the council would do the big decisions.
-Twilight Sparkle: Obviously the superior candidate. Taught from foal by the princess herself and knowledgeable in books and friendship, she was pretty much raised for this. And thanks to the slowness of bureaucracy, even her crazier freak-outs would be unlikely to result in damages before she has had time to think them through.
-Derpy: All royal decisions based on over-simplifications and troll physics. Political scientists around the world spend sleepless nights wondering how it is possible that despite this everything still works out just fine.