Both the Aura HD and Sony have removable storage. The Aura HD chokes a bit on more than 1,000 books though and has recently developed firmware problems relating to books stored on SD card. Sony seems okay with 4000. Probably more.
Aura HD has larger screen and is larger size. I don't find it overly cumbersome to hold, but I prefer the more lighter compact T3 and its nice soft feeling back. I do like the HD touch to turn pages, but the T3 buttons are just as easy.
I display about the same amount of text on either as I find the Sony fonts slightly easier to read and smoother. Kobo has more options but they don't all work and even those that do are of no benefit to me because of their limiting factors.
All epubs display well as can be expected on the Sony, the Kobo is more finicky. Some books have triple line spacing or wide margins for instance on my Kobos but look perfect on my Sonys. I can fix them for kobo with calibre but a PITA and I don't think it is right to de-DRM and change library books.
Kobo updates their firmware fairly often trying to fix older problems and to give us a few new ones to whine about. Sony doesn't, and perhaps they should, but overall the Sony readers are relatively bug free. The T3 has not exhibited any unexpected behavior in the 8 books I have read on it, but I had the occasional issue with the T1. The 600 and 350 did not seem to have any issues.
People speculate that Sony is going out of the ereader market because they are not selling readers in the US and don't have a built in light. Maybe they are but so far it is purely speculation.
Doesn't matter to me in the choice of which reader today. Sony readers have few problems, and AFAIK there support is as good as Kobos. (Amazon is the best support IMO).
I would be sad if Sony stopped making readers, but this just means no new model perhaps next year, or the year after, and has zero importance on what I buy today. Neither Kobo or Sony sell replacement part so what is the difference. Braun doesn't sell blenders in North America any more, but despite that my Braun blenders still function and Braun is still in the blender business. And I'd still buy Braun given a choice.
Overall I prefer the T3 but I may have a low frustration tolerance compared to most. I am sure you would be okay with either. (or a paperwhite
)
Helen