There are two iOS 7 app problems which have yet to be fixed.
Both iBook and Kindle apps lag in handling an open book. That is, I have the app running with a book open, then switch to a different app, then come back to either iBook or Kindle. Both hang temporarily, the screen blanks, a spinner appears, then the current book page. Because both apps do this, I expect it is an iOS problem. I haven't seen a problem with the Nook app.
The second app that is having problems is GoodReader. It crashes, fairly consistently, and I have inundated the develop with the log file it generates. They are still debugging the problem.
How do you switch? I just opened iBooks to an open book page, double clicked the home button to display my other open apps, clicked on music and it smoothly transferred to that display, then double clicked the home button again and clicked on iBooks' icon and it smoothly moved that display back over the screen. Just did the same with Kindle, smoothly moved to the new screen each time, back and forth...