I haven't had any experience with Otterbox iPhone cases, but I would recommend Lifeproof. It's true that there is a little bit of an air layer betwee nthe actual screen and the outer protective layer at the bottom of the screen, but it just takes a few days to get used to. I don't know if that's done intentionally (like that the air is supposed to protect your screen somehow and has been incorporated in the overall design of the case), but it isn't really all that bothersome.
I haven't had any problems with any parts of the case not sticking together. Everything worked fine for me for the first installation, and they have great videos for tutorials that explain how to install the case, perform maintenance, remove the case, test your case for waterproofing, and so on. They also have a large collection of accessories that are compatible with the case as well that are very useful for their specific needs.
The only other issue for me that I had with this case was that the audio jack is only usable with the Apple Headphones that come with the phone itself. The hole built into the case is too small for any other pair of headphones that I have used. It does come with an adapter, but it's cumbersome to take with you, the remotes built into headphones won't work with it, and they are fairly easy to break (mine quit a couple of weeks ago for an unknown reason).
Otherwise, great case, definitely recommendable.
