I agree with Anthem about the Kobo app being prettier. I like the background selection. However, I find the Kobo app problematic. Even after updates that were supposed to contain bug fixes, I still have books that won't open quickly or they freeze the entire app shortly after they do open. I end up having to close the app completely when switching back and forth between books (double tap home button and swipe up). The highlight feature stopped working several updates ago so I gave up on that. I am at the point now where, even with coupon discounts, I'll be choosing books in the Kindle format even if they are a bit more expensive because I'm just sick of the hassle involved with Kobo and epubs. (Bluefire also does not work as smoothly as it should, but I've been using it for epub books that I want to highlight.)
Oh, and having to redownload my library several times after Kobo app updates...not fun.
The Kindle app just works, and it synchronizes smoothly between devices all the time and smooth synchronization between devices is one of my must haves. The only thing I don't like about the Kindle app is when I use it for library books, I have to log into my account on a web page to return the book. But it still beats dealing with an epub version of the books, which won't synchronize between devices no matter what app I use to read it. (Overdrive, Bluefire, or Kobo. Bluefire freezes during attempts to synchronize...again, not worth the hassle.)
I just want to read and enjoy books, I'm not interested in fussing and fiddling with file formats and buggy apps.