Tolkien gives us two very different kinds of heroes in LotR, Aragorn and Frodo. Flieger describes these two primarily within the context of how they fit into and subvert different types of hero journeys, and I will try to build upon this description a bit more and talk about how these two hero journeys (the romantic hero and the fairy-tale hero) subvert the natures of men and hobbits, setting Aragorn and Frodo apart from others of their kind. I will also talk about the extent to which Frodo and Aragorn both fit into our conceptions of immortality and death (despite both being mortal).
The fairy-tale hero, as described by Flieger, is "utterly ordinary . . . He has doubts, feels fear, falters, makes mistakes; he experiences, in short, the same emotions we experience. He is a low mimetic hero thrown by circumstances not of his making into high mimetic action" (Flieger, 124) This doesn't appear to inherently contradict the nature of hobbits, who generally are quite ordinary. They are not generally the adventure-seeking type, and Tolkien says that over time they "grew afraid of [the elves], and distrustful of those that had dealings with them; and the Sea became a word of fear among them, and a token of death, and they turned their faces away from the hills in the west" (Tolkien LotR Book I, 16) As a result, Bilbo and Frodo are considered "very exceptional" given their relatively greater interest in the world outside the Shire, indicated by (among other things) "their friendship with the Elves." (Tolkien LotR Book I, 16) It is this curiosity that sets both of them apart from many of the other hobbits, and that sets the fairy-tale hero apart from hobbits.
The humans of LotR are supposed to be the same as those of our world, and given Tolkien's strong Christian beliefs it's certain that he would say that the humans of Middle Earth are flawed and tainted by evil, just as those in our world are. The romantic hero (and hence Aragorn) seems to transcend much of the flaws of this nature though. In the case of Aragorn, this seems to be at least somewhat attributable to his elvish ancestry (Flieger, 127), which may smooth out some of the natural corruptions in humanity. Despite having flaws of their own, the elves are much more perfect beings than men, and it seems as though many of the most noble characters in Tolkien's legendarium have elvish blood. We can see a similar situation in Eärendil, another romantic hero with elvish blood who transcends normal humanity (albeit to a much greater degree than Aragorn, who is still mortal and nowhere near Eärendil's demigod-like status). The case of Eärendil gives us another piece of data to help to explain Aragorn's larger-than-life nature and how he is able to transcend the flaws we see in other humans in Middle Earth.
Aragorn after the end of LotR reunites Gondor and Arnor, and we know that his son rules the Reunited Kingdom well into the Fourth Age as well. While we don't know this for a fact, his status as king, involvement in the War of the Ring, and reuniter of Arnor and Gondor would have given him renown which would long outlive him, even independent of any records like the Red Book of Westmarch. In this way, while mortal, Aragorn's reputation would in some sense be immortal (at least as long as legends of his reign and deeds continued to be told).
In contrast, Frodo leaves with the elves at the end of LotR for the Undying Lands in order to heal his spirit from the wounds inflicted upon it by the Ring. It's worth noting that in spite of this name, we do know that Frodo one day died (since reaching the Undying Lands doesn't grant immortality to mortals). Moreover Frodo's role in the War of the Ring, while undeniably every bit as important as that of Aragorn, was much more likely to fade into myth than that of Aragorn. Tolkien reiterates throughout his writings that the Third Age was one of mystical parts of Middle Earth fading away. As a result it seems unlikely that Frodo and the hobbits would have the same renown throughout the kingdoms of men as Aragorn, not only because hobbits seem to be commonly seen as myths but also because it seems reasonable that Tolkien believes that eventually the hobbits will fade from Middle Earth, just like the ents and elves, leaving only men.
I've heard a saying that you die twice, once when your body dies, and again the last time anyone thinks of you. If we are to accept this, it seems to me that Frodo's second death is bound to come much sooner than that of Aragorn, whose legend will certainly endure in some form throughout the kingdoms of men. This harkens back to Flieger's point that Aragorn being a larger-than-life mythical hero who is "equal to any situation. We are not like him, and we know it. We admire him, but we do not identify with him." (Flieger, 124) Frodo on the other hand is much more of an everyman, and while he is invaluable in the War of the Ring, because of his lowly origins he is destined to one day fade with the rest of the hobbits.
I don't think Tolkien would have us despair in being unlike Aragorn though. Tolkien explicitly says that "Death is not an Enemy [sic.]" (Tolkien Letter 208) and given how incredibly vital Frodo and the hobbits were in the War of the Ring I don't think that he believes that their humble place within Middle Earth is any less than the grander one of Aragorn. Frodo is incredibly special, as Tolkien says that "few others, possibly no others of his time, would have got [to Mount Doom]" (Tolkien Letter 192) without succumbing to the temptation of the Ring's power. As a result, even though men (and Aragorn) will have a much more lasting impact upon the future Middle Earth, this doesn't mean that we should consider the hobbits and Frodo to be less important than them in the broader scope of the Third and Fourth Age.