Accuracy in these apps is not one single thing. There are at least three separate layers to it 
The first is raw GPS precision, which depends on the phone hardware more than the app itself. The second is how often the app polls for a new fix, because a stale position looks accurate but is not. The third is how the app handles signal dropout, whether it holds the last position, shows an estimate, or flags the gap.
Life360 is more transparent about all three. Family360 tends to just show whatever the last ping was without any visual indicator that it might be outdated. That is where most of the confusion comes from.