I think that's Prince is better then Dark Prince. First off, the Prince has more health then the Dark Prince even with the Dark Princes shield. I don't really see how much of a difference the Dark Princes shield makes because when they are added together (lvl 8 vs lvl 8) there isn't as many hit points as the Prince has. And even though the Dark Prince does have splash damage it doesn't even make that much of a difference. The Prince does more damage then the Dark Prince (could be because of splash damage). And to me it just seems as if the Dark Princes charge is slower then the Princes (opinion). And Prince you can get early so you have more time to level it up but the Dark Prince you have to get alway the way to Arena 7 (2000+ trophies) and it's pretty rare to have in him in the shop or get him from a chest.
I think that Dark Prince is better than Prince. Yes, Prince has more health and more damage but that is offense. Defense is a big part and the Dark Prince has splash damage which means he will have an easier time defending the tower against any troop that spawns more than 1 like barbarians or spear goblins. The reason why the dark prince has a shield is because after the shield is broken, it does damage to troop currently around or attacking the Dark Prince. If the Dark Prince is encountered with a giant horde of troop, he will lose his shield and deal some damage as well as slightly knock back the troops. Supercell said that in the latest update that the Prince and the Dark Prince are the same speed while charging. You say that the Dark Prince requires to get to Royal Arena. That just means that he is a better troop and only people that have been playing lone enough and well enough can obtain him. He is much more rare than a prince which gives people an impulse that he is better.
What? Why would anyone use Dark Prince Asa defensive troop? It is mainly considered as a troop for offense, that is why it has a charge! And can't you just counter a Dark Prince with any air troops (Minion Horde)? And just because Dark Prince is in a higher arena doesn't mean that the troop is better, that's like saying Royale Giant is better then Balloon or Prince. And sorry if that the Dark Prince has the same charging speed (just an idea).
Dark prince is more fit to be used as defense. It costs less elixir and it doesn't do enough damage to do a lot of damage to a tower. Princes cost 5 elixir while dark princes cost 4 elixir and the drop in elixir cost can have a significant effect in the game. Sometimes, you may be encountered with a tower with a low amount of health with little time left in the game. Sometimes waiting for 5 elixir can affect your game like in the end if there is only 3 seconds left and a prince is charging to win the tower, you can put down a dark prince in front to act as distraction if you don't have enough time to put down a prince. You note that the dark prince is mainly known as an offensive troop just because it has a charge, but it might be used to do harm small troop that may have more health than the regular attack damage. For example some people use the dark prince and prince rush and what is the dark prince used for? Defense for the prince. The prince is the main form of damage while the dark prince protects the prince from small troop that would usually counter the prince. You say that dark prince can easily be countered by air troops but isn't that what prince is countered with too? They are both easily taken out by air troops that the prince can't attack.
First of all, saying the Dark Prince was more of an offensive card was just an example so it isn't really worth attacking. And you don't have to use Prince to take out an arena to were with low health, there are other cards such as rocket or hog rider. And you said that both princes can be take out by air troops, EXACTLY!! It isn't really worth having less health and damage so you can do splash damage if you know you're going to get taken out by air troops.
I know that there are other ways and the prince is just an example of when you might need a lower elixir troop as distraction. For example you could also be attacked by spear goblins, goblins, musketeer etc. You also said that there is no point for splash damage if you know your going to be attacked by air troop but that is the same as, why would you have more damage and hitpoints if you know you are going to be attacked by air Troops? Though if you used Dark Prince as defense, you would be able to see the minion horde before it could kill you which would allow you to arrow the horde.