Mobyaffiliates has a great new list of 2013 Mobile App Analytics Tools.
My experience of 3rd party analytics tools are that they are great for getting something going quickly. Analytics are (sadly) nearly always the lowest priority during development but this suddenly changes at the end of a project or after the app has shipped when the product owner realises their oversight.
While quick to set up, once you need 3rd party services to do more specific things it either gets costly or what you want to do just isn’t possible. I have also found some clients don’t like the idea that a 3rd party knows what’s going on inside their app. There’s also the slight worry what will happen to the app if the 3rd party stops providing the service or messes up and makes a new API incompatible with an older one used by the app. This is obviously less likely to happen with the larger/more mature 3rd party providers.
Product owners (and us developers) also need crash analytics that only some 3rd party providers are starting to provide. For some reason, the Mobyaffiliates listing doesn’t mention Crittercism that I have used on a few projects and is fairly popular. Also consider open source solutions such as ACRA (on Android) for crash analytics reporting. I have found ACRA particularly useful for sending extra information that doesn’t appear in the Google Play console crash analytics. Don’t forget you can also implement your own analytics solution that can tie into your existing server API that’s easier done during the project than as an afterthought at the end.