Ghost, Frog, Robot, Fairy: The Metamorphosis of the Ultimate Self
Adapted from an original post on /r/homestuck
Once I got to really thinking about the Epilogues, one of the things that started to stick out to me very quickly was that it seemed kind of arbitrary who got to attain their Ultimate Self and who didn’t. Why Dirk and Rose, and not other high-power characters like Vriska and John?
But now it’s hit me; what connects Rose and Dave and Dirk all together, other than familial relation, is that they all spent time as a sprite.
Why is this significant? First of all, the ascended essence of a person is compared directly to a kernelsprite in the epilogue;
The second thing that came to mind was a specific exchange between Kanaya and Aradia, where they’re talking about transformations:

AA: you are undergoing a metamorphosis which you have been groomed for since you were very young
AA: much like i was for my various personal iterations including this one
GA: You Mean
GA: Being A Ghost And Then A Frog And Then A Robot And Then A Fairy
AA: yes!
This dialogue was fresh in my mind because I’d recently seen it suggested that it was a reference to Lord English, and his being composed of a ghost (sprite), frog (cherub), robot (AR) and fairy (Gamzee). But with the Epilogues in mind, I think the significance of that line may go deeper, and refer to the stages of transformation that culminate in the Ultimate Self.
The ‘ghost’ stage still refers to spritehood; ‘frog’ could be combined back into the sprite stage (or just as easily replaced with ‘cat’ or ‘bird’ or ‘troll’ for Rose, Dave or Dirk) or taken as a reference to the creation of the new universe. And that’s why Rose and Dave are put into robotic replacement bodies; because ‘robot’ is the next stage in the metamorphosis.
That also seems to be why Dirk is able to handle the ascension process, or at least reacts differently to it; because splinters of him have already manifested as sprites and as robots (you could argue that the version of him that became a sprite, AR, was also a robot himself).
The involvement of sprite selves is especially important because it’s the sprite version of Dave that first brings up the concept of the Ultimate Self:

The last two lines convey essentially the same reasoning as Dirk’s for putting Rose in a robotic replacement body; the physical, organic body can’t handle the strain of all of its selves, but other, more advanced bodies can.

The very nature of the sprites involves a property that is far more relevant to the realisation of the Ultimate Self, though, which basically went undiscussed until Homestuck: Book Two, which contains the following commentary on page 251 of Homestuck:
The concept of prototyping in [SBURB] was always about distilling the prototyped elements into something more symbolic, more essential, and customizing the whole game according to the merged ideals of those components. Just a bit more of this Platonic nonsense that kind of goes unspoken, that is up until these books, when I had to go and totally de-unspeak it like a friggin’ loudmouth.
Andrew mentions this “Platonic nonsense” again in the commentary for page 1810, which helps clarify the point:
…in this particular fictional realm, and especially where alchemy is concerned, the fundamental ideas the objects represent are more important than the objects themselves.
With this context, the importance of the kernelsprite in the metamorphosis becomes extremely clear: while the various splinters and selves of a person are merely reflections of a fundamental idea, by being prototyped, a person becomes the very idea that they represent.
Something that was frequently the point of conversation when the sprites^2 were first introduced was the fact that their designs incorporate dream pajama elements, even though none of their components were dream selves. The Ultimate Self being the end goal of existence offers some answers to this:

Dream selves can be used to absorb part of your self from another timeline, and are instrumental to the process of reaching the god tiers; so it makes perfect sense that a special kind of dream self would be involved in the ascension to the Ultimate Self.
I’m not forgetting that Jade has also been a sprite and a robot; but thanks to her special connection to the Dead Cherub, it appears she’s going through a much different ascension to the other characters. By literally eating her brother in the Meat Epilogue’s postscript and subsequently powering up, it appears the cherubic definition of ‘absorbing alternate selves’ takes on a far more literal meaning.
So with this in mind, the two parties formed by the end of the Epilogues seem to be composed of characters who have all been through - or are in the process of going through - the same sprite, robot, fairy metamorphosis: the original, Aradia, alongside Jade and Dave, and Dirk alongside Rose, as well as Terezi, who absorbed her ultimate selves in her own way, and John, whose status at this point is all but unknown.