Besides what the App Store provides, privacy policy inspection is typically done manually for iOS apps.
I utilize a DNS blackhole to create a transparent proxy while running Network Miner and using a pluggable logging proxy to replay SSL/TLS or other encrypted protocols. Mallory is often cited as a great pluggable logging proxy, but I prefer Burp Suite Professional because I often perform additional tasks with this tool. Note that this DNS blackhole method will not catch IPs that do not perform name translation, although a sniffer will still pick that traffic up.
A better method might be to inspect the source code during and after building it (when available). I use xcodebuild (along with clang-analyzer and Fortify 360 SCA sourceanalyzer) and Flash Professional to handle much of this work. The smartphonesdumbapps analyze_ios.pl tool is also quite excellent.
There are many tools for tracing execution when using the iOS Simulator, such as dtruss, iprofiler, Instruments, iosnoop, execsnoop, the DTraceToolkit, etc -- all of which really rely on the OS X version of DTrace. These are not as available on device, which supports gdb (XCode also automatically attaches lldb to the iOS Simulator or device when successfully building the code from the GUI).
If you want to see the Objective-C runtime on device, I highly suggest cycript.
Apple's policies regarding Contacts and UDID are changing rapidly. I do not believe that Apple's policies can be relied on, as many malicious apps have been made available through their App Store throughout its existence. Yes, less than Android -- but it still has happened.
A few Android apps that perform this type of inspection do exist, such as TrevE's Logging Checker, and the many apps from Lookout Mobile Security. I do not find these tools to be perfect, and perform a similar analysis as the iOS one using similar tools (strace instead of DTrace, Android Emulator instead of iOS Simulator, Android SDK instead of xcodebuid, Eclipse ADT instead of XCode GUI, FindBugs instead of clang-analyzer, etc).
I'm sure we'd all love to have Lookout Mobile Security app equivalents on iOS, as well as a cycript implementation for smali on Android.