I use my Kobo Touch mostly for fanfic. Calibre has a plugin that can pull stuff directly from AO3 and other fic archives -- it works great. Or you can download epubs manually from AO3 and add them thru Calibre, it only takes seconds. I don't use wifi on my Kobo so I can't comment on direct browsing.
For what it's worth, the downsides I've found with the Kobo as a fic reader are:
(1) Doesn't display summaries (though Calibre does).
(2) Doesn't display or use tags (though Calibre does).
(3) Organization can be iffy. I use Shelves (easy with Calibre and the metadata plugboard) but each book/fic can only be in one shelf -- there's no way to add it to multiple shelves (as far as I know). So deciding how to set up your Shelves takes some thought. If you only read one fandom, for example, you could set up shelves by genre & pairing; or if you only read one pairing, by genre & rating. Etc. Whatever works best for your collection.
(4) Probably just a personal annoyance :-) but there's no title (or author) display while you're reading. I'd love if a future Kobo update could put the title in small font down where the page number is, or at the top like a paper book. I read a lot of fic and sometimes I get halfway through a story and totally forget the title & author!
Hope that helps. I haven't tried out the Sony readers but I've been curious about them, for the reasons above.