I don't know how apple manages it but the new testflight is a pain to use.
The process of adding a tester alone is not intuitive and requires way too many steps.
I switched to installrapp.com for testing iOS stuff because I don't have the time to spend on finding out why the app I released for testing is not showing up in my clients test flight.
I've been using Beta by Crashlytics as it is nice and cross-platform and works with ios7. Downside is the integration process and management console are a little tricky.
Crashlytics (now owned by Twitter and rebranded as 'Fabric') is great. I'm surprised you thought the integration was tricky as it's the most simple setup I've seen. You install a menu bar app that literally walks you through each step and which automatically grabs your archives (when you archive a build) and lets you send it to testers in a couple of clicks.
I just got 2 emails today from the legacy testflightapp.com, reminding me that they are shutting down the site on Feb 22 and that I no longer will be able to access all my historical tester-app data. The email provides instructions for migrating the data from testflightapp.com to itunes connect (which is always a pain to have to go through). When I went through the steps in the email, it seems as if all the previous accepted testers would have to re-accept the testflight process. I hope this isn't the case, but it's not the end of the world otherwise.
On a larger theme, I'm surprised that someone (an enterprising tech person) doesn't set up a service that archives all the data from startups that get acquired and then are shutdown. I'm imagining something like a secure github that has all the channels for each dead/acquired service that you could log into. Or perhaps there could be a company that charged the acquirer a small fee to take over the hosting of just the archived data, so it's still accessible. Perhaps this already exists?
The process of adding a tester alone is not intuitive and requires way too many steps.
I switched to installrapp.com for testing iOS stuff because I don't have the time to spend on finding out why the app I released for testing is not showing up in my clients test flight.