Like in just about every question of Judaism, there's more than one explanation/opinion.
Ramabm (Moreh Nevuchim 2:45) and Radak (intro to Tehillim):
Expounding upon the Gemara (Berachos 4, Pesachim 117, Megillah 7), they say that the reason for the difference is that the prophecies of the books of Navi were written in a higher level of prophecy than those of Kesuvim. Rambam and Radak both explain that there was an actual difference: the prophet of navi would fall asleep and have a vision, while the author of kesuvim would write while 'inspired' while awake under divine inspiration. R. Bachya (Vayikra 8:8) develops this idea as well, that the prophet of navi was removed from physicality during his vision, which wasn't the case with authors of kesuvim. (And it's possible for higher-level prophets, even Moshe, to also sometimes receive lower level prophecy, which is how he can be credited with writing Iyov.) Radak also adds (in his intro) that Divrei Hayamim was added to Kesuvim because it's mainly about history.
R. Menachem Meiri (into to Tehillim):
He rejects the Rambam, 1) because Tehillim and Daniel have real prophecies in them and 2) because the same people who were prophets also wrote Kesuvim. Therefore, he says that the difference is in purpose or context: Neviim were written by prophets who were specifically sent by God to admonish the people, and the Kesuvim/'writings' are just that; containing advice, poetry, and history (future history is also history).
Abarbanel (Mayyanei Hayeshua 3:2)
has a similar approach as that of the Meiri, as he states that the entire difference was in mission. Neviim were people whose mission it was to go out and prophecize among the people, and Kesuvim were prophecies that God instructed them to write down.
Netziv (Haamek Sheilah, intro to Sheiltos no. 8)
The Neviim were written in 'the language of God' (which I assume means more flowery/metaphorical, though I'm just guessing here), and the Kesuvim were written in the language of man.
Chiddushei HaGrach vehaGriz to Bava Basra 15a:
R. Chaim of Brisk was recorded as saying that the Neviim were instructed to first state their prophecies orally, and then write them down, while the authors of Kesuvim were instructed in the reverse: to write their prophecies and then read them from a text. (I'm not sure what to make of the theological significance of this difference) However, R. Chaim's son R. Yitzchak Zev had several questions on this explanation.
R. Yitzchak Hutner (Pachad Yitzchak Shavuos 2)
While the levels of the divinity of prophecy (and therefore their holiness) may be the same, Kesuvim represent a more 'hidden' form of prophecy, and Neviim are more openly revealed (which I assume means easier to understand; this may be the opinion of the Netziv quoted above).