I don't have any familiarity with the other apps in this space, but I am a heavy (and happy) user of OurPact. OurPact adds a lot of parental management features (including a remote kill) which the Apple controls are desperately missing.
The backup is taken at install time and it's perfectly reasonable to do so. The backup is stored local on your computer using the standard backup mechanisms, it's not uploaded to the cloud.
The installation process is actually opting the device into an enterprise management profile, not a custom OS. That custom OS blurb sounds like some goofy marketing speak or misunderstanding how this process works. The management profile allows OurPact to manage the device on your behalf using the same APIs any enterprise device management vendor would use.
Once the device is opted into the management profile, it's quite obvious it's under control and you have a lot of options including setting time limits on app, enabling various child protection features, preventing apps from being deleted, and most importantly choosing what apps are available and creating schedules for the device (i.e. disabling games during school hours/night).
Nothing about this process hides the fact that the device is managed. There is an OurPact Jr app that can be installed which gives the owner visibility into the schedule. I highly recommend reading the reviews by upset children for the OurPact Jr app on the app store. They are hilarious.
Anyway, my point is as a parent with a tech background and 3 children, OurPact has been a very useful and positive addition to our home life. They've been a good steward. They are limited in what they can do by Apple, but what they have done they have been very transparent and communicative.