On Berachot 63a-b, we had the following:
R. Safra said: R. Abbahu used to relate that when Hananiah the son of R. Joshua's brother went down to the Diaspora,38 he began to intercalate the years and fix new moons outside Palestine. So they [the Beth din] sent after him two scholars, R. Jose b. Kippar and the grandson of R. Zechariah b. Kebutal. When he saw them, he said to them: Why have you come? — They replied: We have come to learn Torah [from you]. He thereupon proclaimed: These men are among the most eminent of the generation. They and their ancestors have ministered in the Sanctuary (as we have learnt: Zechariah b. Kebutal said: Several times I read to him39 out of the book of Daniel). Soon they began to declare clean what he declared unclean and to permit what he forbade. Thereupon he proclaimed: These men are worthless, they are good for nothing. They said to him: You have already built and you cannot overthrow, you have made a fence and you cannot break it down.40 He said to them: Why do you declare clean when I declare unclean, why do you permit when I forbid? — They replied: Because you intercalate years and fix new moons outside of Palestine. He said to them: Did not Akiba son of Joseph intercalate years and fix new moons outside of Palestine?41 — They replied: Don't cite R. Akiba, who left not his equal in the Land of Israel. He said to them: I also left not my equal in the Land of Israel. They said to him: The kids which you left behind have become goats with horns, and they have sent us to you, bidding us, 'Go and tell him in our name. If he listens, well and good; if not, he will be excommunicated. Tell also our brethren in the Diaspora [not to listen to him]. If they listen to you, well and good; if not, let them go up to the mountain, let Ahia1 build an altar and let Hananiah play the harp,2 and let them all become renegades and say that they have no portion in the God of Israel'. Straightway all the people broke out into weeping and cried, Heaven forbid, we have a portion in the God of Israel. Why all this to-do? — Because it says, For out of Zion shall go forth the law, and the word of the Lord from Jerusalem.3 We can understand that if he declared clean they should declare unclean, because this would be more stringent. But how was it possible that they should declare clean what he declared unclean, seeing that it has been taught: If a Sage has declared unclean, his colleague is not permitted to declare clean? — They thought proper to act thus so that the people should not be drawn after him.The parallel in Yerushalmi Nedarim 23a-b reads as follows. I'll pull it from the excellent Yedid Nefesh Yerushalmi, which is like a Hebrew Artscroll for Yerushalmi, where the work is already complete. (Artscroll in the sense of running translation and halacha at the bottom, but not with Artscroll's footnotes.)
Yirmeyahu [haNavi] intercalated in Chutz LaAretz. Yechezkel [haNavi] intercalated in Chutz LaAretz. Baruch [ben Neriah, Yirmeyahu's scribe] intercalated in Chutz LaAretz.
Chanania the son of the brother of Rabbi Yehoshua [ben Chanania] intercalated in Chutz LaAretz. Rabbi sent him three letters via Rabbi Yitzchak and Rabbi Natan. In one of them he wrote, 'to the holiness of Chananiah'. And in one of them he wrote, 'The kids which you left behind have become goats with horns.' And in one of them he wrote, 'if you do not accept upon yourself [the times set in Eretz Yisrael] go out to the wilderness of thornbushes, and slaughter there, and Nechunyon will sprinkle [the blood of the korban].'
Rabbi Yitzchak [the agent] arose and read [perhaps in a derasha]: It is stated in the Torah, "Eleh Moadei Chanania son of the brother of Rabbi Yehoshua". They [the tzibbur] said to him [correcting him]: By us [is written] Moadei Hashem! He said to them, [only] by us [but not by you]!
Rabbi Natan [the other agent] arose and finished: Ki MiBavel Teitzei Torah Udvar HaShem MiNehar Pekod. They said to him: Ki miTzion Teitzei Torah Udvar Hashem miyrushalayim! He said to them: By us!
He [Chanania] went to Rabbi Yehuda ben Beteira in Netzivin [to complain]. He [R' Yehuda ben Beteira] said to him: After them, after them. He said to him: Don't you know what I left there [in terms of the low caliber of Talmidei Chachamim there]? Who will tell me that they are Chachamim who can calculate as well as me? [R' Yehuda ben Beteira answered]: Since you say that they do not know how to calculate as well as you, they should listen to you? Rather, since they say that they are Chachamim [alternatively, knowledgeable to] calculate like you, you should listen to them! He [R' Yehuda ben Beteira] arose and rode on his horse. To the places he reached, he reached [and they followed his advice]. To the places he did not reach, they acted inappropriately.
It is written [in Yirmeya 29:1]:
|א וְאֵלֶּה דִּבְרֵי הַסֵּפֶר, אֲשֶׁר שָׁלַח יִרְמְיָה הַנָּבִיא מִירוּשָׁלִָם--אֶל-יֶתֶר זִקְנֵי הַגּוֹלָה, וְאֶל-הַכֹּהֲנִים וְאֶל-הַנְּבִיאִים וְאֶל-כָּל-הָעָם, אֲשֶׁר הֶגְלָה נְבוּכַדְנֶאצַּר מִירוּשָׁלִַם, בָּבֶלָה.||1 Now these are the words of the letter that Jeremiah the prophet sent from Jerusalem unto the residue of the elders of the captivity, and to the priests, and to the prophets, and to all the people, whom Nebuchadnezzar had carried away captive from Jerusalem to Babylon,|
Hashem said: More [yeter] are they dear to me, the zekeinim of the Diaspora; yey the smallest kat [set] in Eretz Yisrael are dearer to me than the Sanhedrin outside the land.
But it is written [II Melachim 24]:
|טז וְאֵת כָּל-אַנְשֵׁי הַחַיִל שִׁבְעַת אֲלָפִים, וְהֶחָרָשׁ וְהַמַּסְגֵּר אֶלֶף--הַכֹּל, גִּבּוֹרִים עֹשֵׂי מִלְחָמָה; וַיְבִיאֵם מֶלֶךְ-בָּבֶל גּוֹלָה, בָּבֶלָה.||16 And all the men of might, even seven thousand, and the craftsmen and the smiths a thousand, all of them strong and apt for war, even them the king of Babylon brought captive to Babylon.|
[which is darshened in praise of Talmidei Chachamim of the Diaspora, who silence all others in their Torah wisdom] and you say this?!
Rabbi Berechia citing Rabbi Chelbo, and the Sages [each resolved this]. Rabbi Chelbo said: The charash were a thousand and the masger were a thousand; and the Sages said: in their entirety they were a thousand.
Rabbi Berechia citing Rabbi Chelbo said: These were the Chaveirim [Sages]. And the Sages said: These were the important officials."
End translation of the Yerushalmi.
What is this business of setting up one's own altar, which features in both Bavli and Yerushalmi. See sefer Yehoshua, perek 22, where Bnei Gad, Bnei Reuven, and half of Shevet Menashe, built their own altar there. It was as close to 'outside the land' as they had at the time, and it seemed like they were going to go it alone and sever their connection from the rest of Klal Yisrael. I will reproduce it here:
This is why Bavli features the assertion that they should declare that they have no portion in the God of Israel. See pasuk 25 and 27.
I would add that there are some rabbis (and in fact, some people who have communicated with me privately by email) who make a similar assertion -- that in halacha, we must now all follow the "Gedolim" in Eretz Yisrael, because of the idea of Ki Mitzion Teitzei Torah. Here is an example.
Besides that I don't know that the Gedolim in Eretz Yisrael are as competent to pasken, especially in matters pertaining to metzius, which requires a knowledge of madda that many are unfortunately lacking, I don't know that this Bavli and Yerushalmi are discussing any more than setting the moadim, where a unity of religious calendar of when Yom Tov is at stake, and a fracturing will create two different communities that cannot interact. But differing piskei halacha have always been in place.
And further than that, we have the precedent of the Amoraim of Bavel and Eretz Yisrael. There were Sages in both places, and yet the Sages in Bavel quite often paskened against the shittot of the Sages in Eretz Yisrael.