Stache does offer its own in-app browsing, but it lacks the extra features and speed found in Safari. It's fine for quickly getting to a Web page if you start with Stache, but it's nothing special.
Looks better than Safari
According to its listing in the iOS App Store, Stache is designed to make it easy to view and find your favorite bookmarks. About this I absolutely agree. Each listing is displayed as a screenshot of the page you saved, making it really simple to identify each bookmark. It's a much better experience than you'll get on Safari, and more aesthetically appealing.
In Safari, for example, Apple's plain text list makes it harder to browse, and the titles of longer bookmarks can be truncated. The latter point can be especially annoying considering that Safari bookmarks are displayed only as a text list.
In the end, while Stache is better for browsing bookmarks, Safari remains better for saving them. That's why in the end I'd say that Stache still isn't worth the trouble.
iOS 8 is coming soon
One thing that might help this app is a feature coming in iOS 8. At the announcement at WWDC, Apple said iOS 8 will let developers use extensions to allow apps to extend functionality to other apps. So, presumably, a lot of the objections I have to Stache's method for saving bookmarks could be eliminated once it's upgraded for iOS 8. If the features work as advertised, you would probably need to "allow" a Stache bookmarklet to be added to Safari, getting rid of the confusing setup process.
I wanted to like Stache because I'm eager to find a better method of managing both bookmarks and pages I want to read later. Sadly, Stache isn't it. At least not yet. The procedure for getting bookmarks into the app is just too much of a hassle. The Stache website claims the easiest way to add bookmarks is to use a Mac. But what about people who don't have a Mac? Or those who don't want to shell out another $7 just to save bookmarks?
I like what the team did by using thumbnails to display the pages you've saved and providing a way to search for items, but Stache simply needs to be easier to use for it to be worth your money. Hopefully the new features coming in iOS 8 will help.