אליהו הנביא הגדול בנביאים אחרי משרע"ה
That Moses was the greatest prophet is hardly controversial. It is attested to in Scripture and enshrined into fundamental Jewish theology by Maimonides.
Elijah is probably the most famous prophet in Judaism. This is probably due to his involvement, according to various traditions, in Jewish life throughout the millenia – attending circumcisions, drinking wine from every house on Passover Eve, hanging out with some of the Sages in the Talmud as well as the Hasidic masters, etc.
The question is, though, is there anything to indicate that he was actually the greatest prophet after Moses? Whence did R. Emden know this?
In fact, perusal of some other parts of rabbinic literature leads to a different conclusion. R. David Kimchi, in his commentary to Psalms 99:6 writes that Samuel was possibly the greatest prophet after Moses, and in his commentary to Jeremiah he states this definitively and cites several verses that could be indicative of this:
וזכר שמואל לפי שהיה ממשפחת משה ואהרן ונביא כמו הם ואפשר שהיה גדול בנבואה משאר הנביאים אחר משה, וכן אמר אם יעמוד משה ושמואל לפני
והגדול שבנביאים אחר משה רבינו היה שמואל וכן אמר משה ואהרן בכהניו ושמואל בקוראי שמו ונאמר כי נאמן שמואל לנביא לה' ונאמר ולא הפיל מכל דבריו ארצה
R. Kimchi's ranking is perhaps supported by the Midrash Tanchuma which refers to Samuel as "Master/Teacher of all the prophets":
Leviticus Chapter 21
שמואל [רבן] של כל הנביאים
Beyond this, though, are there any authoritative sources that discuss prophet rankings (the earlier the better)? Either in support of, or contravening, R. Emden's view or R. Kimchi's view?
Interestingly, R. Emden's statement has been edited out of most editions of the Talmud. The only edition I was able to find it in was the Nehardea Talmud. Below is an image showing the Nehardea edition with the statement of Elijah's rank, followed by an image showing the Oz V'hadar edition with the part about Elijah's rank missing. That many of R. Emden's Talmudic comments have been censored/edited/concealed has already been pointed out by R. Jacob J. Schachter in his dissertation on R. Emden:
Jacob Emden: Life and Major Works Chapter 2 Note 60
These novellae differ from Emden's Hagahot 'al ha-Shas printed in the back of the standard Vilna edition of the Talmud. Those comments represent a partial transcription of Emden's marginalia on his personal copy of the Talmud, presently found in the Jewish National and University Library of the Hebrew Universit in Jerusalem (Heb 4o 181). See Y. Yoel, "'Osef Kitvei-Yad bi-Bet Dfus Rom," KS XIII (1937), 521-522. Even a cursory comparative study indicates that not everything written by Emden in the margins of his private books was included in the Vilna edition.