As far as I can tell, the only 100% accurate tracking is occurring with Facebook Mobile App Install ads since they have an integrated solution with the App store. But there are many 3rd parties that claim to do it, but my understanding is that it's a "correlative" confirmation, not a true confirmation. Which is the best?
I wanted to clarify something, as a co-founder of one of these tracking companies (Tapstream, we do attribution tracking for free): when you're tracking installs from most ad networks, be it Facebook or someone else, the accuracy will be near perfect with most tracking providers. Ad networks in general support the use of IDFA or Google Advertising ID for attribution, which is passed to us on click. We then collect the same ID on install and send it back to the ad network so they know an install happened from that click. There's no guessing or fingerprinting involved.
If you're seeing divergent numbers you need to examine the whole chain for breakage - your ad network, the attribution solution and lastly, but most importantly, your tracking implementation.