The gemara [Krisus 5b] derives from a special pasuk that a kohen gadol ben kohen gadol requires משיחה. The gemara further teaches that a melech ben melech doesn't require משיחה because the position is inherited and automatic, so משיחה upon appointment is unnecessary.
The Yerushalmi [Horiyos 3/2] says the exact opposite: The law that a melech ben melech doesn't require משיחה is derived from a special pasuk while the law that a kohen gadol ben kohen gadol does require משיחה is derived from the fact that it is an inherited position so it must require משיחה.
For the law of a מלך בן מלך [no משיחה] the בבלי doesn't need a pasuk and the Yerushalmi does. For the law of כהן גדול בן כהן גדול [requires משיחה] the Bavli finds a pasuk while the Yerushalmi does without a pasuk.
What is the nekudas hamachlokes?
The Rogochover talks about it. Rav Mann in the באר מרים [Melchim פ"א ה"ז] has a brilliant mehalech. If this whole blog came into the world so that one person will start learning Rav Mann's sefarim it will have been worth it.
I just fear that I give mareh mekomos sometimes and people just ignore it, go on with their day, check out a few twitter accounts and eat some watermelon. My goal is not to impress you with my scholarship but to promote further learning. After 43 years on earth I have learned [actually I learned it long before] that impressing people is with knowledge is like trying to lead people into thinking that you have a lot of money when you don't. It means nothing. You have to pay the food bill but don't have the money. What does it matter that your neighbor thinks you are loaded like Donald Trump? People thinking you are learned is nothing. What does it do for you?? A shidduch? I already have one. A shidduch for my kids? Sadly, people are generally far more interested in how much money the father of the girl has than how many sfarim he has written. My mechutan is going to want my money a lot more than my Torah [unless I am really lucky and he doesn't need it or care about money]. So what am I left with?
That I want readers of this blog to learn more, both in quality and quantity. THAT is one of my agendas. My others are that people should live lives of kedusha, ahavah [of Hashem, Torah and Am Yisrael], and constantly grow in emunah and middos tovos. There you have it.
You know my agenda.