#also actually

Dune is sci-fi -- prophecies aren't real (for the most part). So the prophecy that the Fremen believe in was actually seeded by the Bene Gesserit centuries ago as a 'surprise tool to help us later' for any Bene Gesserit who might find herself in trouble on the planet.

WoT is fantasy and prophecy is very real, though not always interpreted correctly. The old Aes Sedai who tells the Aiel their prophecy for the future was very much on the level and trying to do her best to protect and save the Aiel rather than setting them up to be manipulated centuries down the road.

The Aiel (at least the leaders of the Aiel) are also very aware that they are meant to be tools in the hands of their prophesied figure and that only "a remnant of a remnant" will survive. They have been explicitly setting up their society as a tool, I would argue, by telling their people that the Three-Fold Land's purpose was to shape them to make up for their 'sin' against the Aes Sedai. So there's a self-awareness to their choices, even in the beginning. They know that their savior is also their doom and walk into it with their eyes open.

This is also a big difference in Paul himself and Rand, in that Paul is a manufactured savior and Rand is a real one -- a large part of that lies in that Paul is a sci-fi protagonist and Rand is a fantasy one (though we could always bring up Paul's son, Leto II, who becomes monstrous in order to try to save humanity from an existential threat).

Paul is a critique of the white savior trope -- he is a complete outsider to Fremen society, takes them over using lies that exploit their religious beliefs, and uses them to further his own agenda, destroying them in the process.

Rand is half-Aiel, so that makes him more akin to Paul's children with Chani than to Paul himself in that regard, in that he does have that blood connection to the Aiel (which lets him experience their history through the glass columns), but he wasn't raised by them, so there's that distance too.

But both Paul and Rand are very aware that they are using the Fremen-Aiel as a tool for their own plans (but again, here I loop back to the intentionality -- not only do the Aiel leaders know this all along, but Rand reveals to all of the Aiel the truth about their past, which means that they immediately fracture in a way that takes the Fremen years to begin doing), so they have that in common.

In addition to the difference between sci-fi and fantasy, we also have a big difference (in the books) in how the two sets of books examine religion. Religion is a much bigger and more explicit thing in Dune than in WoT -- Paul is able to build his following by exploiting his followers' religion to turn them into fanatics. Now we do have an example of some of Rand's followers turning into fanatics, but it's not in the Aiel but in Masema and what he does on the west coast, and the Dragonsworn are mostly not focused on, especially not in Rand's actual plotlines.

But, yeah, Paul Atreides, Rand al'Thor, (and I add Anakin Skywalker) kinda all exist in this sort of venn diagram in my head that I'm going to try to plot out: