Let's generalize that it is a reading app, so one of the principles we are following is to keep it simple, intuitive and with the text in focus. The example shows something like a "song book", but there are other types too.
The current design uses a navigation drawer and the proposed design ( a quick mockup using developer tools ) uses a tab based navigation. So there are some problems:
- Almost all¹ older designs uses navigation drawers, so users are already used to it. In the other hand possible new users aren't.
- It need to be adapted to be easy to use on using only the mouse, only touch or only the keyboard: some users prefer just to use the keyboard, others just use it when searching, and on mobile there's only touch.
- Have a persistent search box like Google Developers/Tumblr designs, a dedicated page like Google Design, or a expandable search box, like many applications?
- Showing the page title showed to be important, but it's a good idea to replace the website name or there is other place to put it?
Even if unrelated to this change, related navigation is also a problem: sometimes users want to navigate between pages like as "I remember it happened somewhere next to this page, but I as don't remember anything else thus I can't use the search, so I will browse page per page". The problem is that most put those links below content, making it hard to access.
Finnaly, it's a website to be used as a desktop, mobile and "TV" application: the design between those modes need to be at least similar. One problem is the homescreen: as all content is text, designing it is a quite hard. Book covers seem to be a good idea, but sometimes it's too simple.