After having installed XBMC on my media server, I tried many different apps on iOS to stream movies, music and series to my iPhone and iPad, but none of them were able to play everything correctly. When the iOS 7 Jailbreak came out a few days ago, I tried installing XBMC via Cydia and it worked like a charm. After adding my media server, I was able to stream even 1080p videos at 48 fps without any problems.
To install XBMC on iOS, open Cydia, go to the tab "Manage", click on "Edit" and then on "Add". Then, enter "http://mirrors.xbmc.org/apt/ios" into the now appearing text field and click on "Add Repository". Cydia will now add the source named "teamXBMC" to the list of repositories. Click on this new repository and then click on "XBMC". You can now install XBMC.