Okay, here's a quick three-way comparison between the Kobo Aura One as well as Kindle Voyage and Oasis:
http://imgur.com/a/04V1N
I tried to keep brightness normalized, and since I didn't have much time to set up the focal plane isn't always 100% dead on, hence the slight deviations in focus between lines. Sorry about that. I also should mention that because of the different controls, it wasn't possible for me to match type sizes 100% between the Aura One and Kindles, so the Aura One text is set ever so slightly larger. Everything is in Bookerly though.
I'll give you my interpretation, but I will preface it by saying that these nuances are absolutely 100% impossible to discern unless your nose is glued to the screen and that either of these screens render text in a very pleasing, eminently readable manner.
That being said, my impression is that the Aura One renders bowls and counters with less visible aliasing than the Oasis, but it's also marginally less accurate to the typeface than the Kindles. You can see it especially in the terminals, which appear thicker, with less defined angles. This could be the result of the way anti-aliasing is handled. The result looks sharper up close, so it seems like a smart compromise.
Of the three, I think the Voyage actually has the crispest rendering, but it might just be a matter of individual unit variances. Both Kindles err on the side of sharpness, which results in super crisp looking text from normal viewing distances but very visible aliasing along curves when you look at it at 1:1 like this. The Voyage also appears to have ever so slightly more contrast.
Anyway, pixel peep away folks!