Based on my experience with the Manga 2.0 app on iOS, on an iPad mini.
To be honest, while the updated app is quite usable, I'm a bit disappointed with it.
The only real improvement for me, given the way I use the app, is that the grid format for bookmarks is better because it takes less time to scroll back to the oldest bookmarked titles when you've got a lot of things bookmarked (as I do).
As to the push notifications, this is either not working for me, or I've not got anything that's been updated recently. Since I've seen some other comments about this elsewhere, I suspect it just might not be working.
Feature enhancements I would like to see:
1) Get rid of the scrolling banner that shows featured manga at the top of the main Manga page, or make it possible to have another view be the first one a user sees when opening the app (such as favorites). This fast flipping display is pretty annoying and the first thing I want to do when I see it is go anywhere but that page (though I do note that simply scrolling down works too) to get it out of view.
2) Add a true sort option that gives you the ability to view all titles alphabetically. Right now the "Sort" option is misnamed; it's not really a sort, it's a filter.
3) Show the "New Chapter" indicator in list view (which is what you first see on the page); not just in grid view (which you have to specifically choose).
4) Make it more clear what order the different "sorts" are in. Within each category are they in order of last update, popularity, or what? I find the "Recently Launched" category to be especially confusing since that is one I'd expect to be ordered by either most recently added title or most recently added chapter, yet it seems to be neither.
1) Allow users to move things around in their own preferred order. At the least provide some basic options such as alphabetical or last updated date.
2) It would also be useful to have a "New chapter" indicator in this view.
1) Add a list view in addition to the grid view.
2) Although I'm happy with the way the most recent bookmark is at the top, I think some might find it useful to have this sortable by title or by date updated.
Overall--personal colr preference. I miss the orange bookmarks. Orange says "Crunchy" to me; blue does not. This is also true for other places where blue is used. I'd rather see orange.