How much caches do they contain? Which device have you got, and can it handle those caches?
The files are just way too big for BaseCamp...
You can't compare it with the number of geocaches in GGZ files, because those are designed to contain large numbers of caches by using indexes. BaseCamp doesn't support GGZ files; maybe a BaseCamp developer will tell whether it is on the to do list or not.
Note that every geocache on the device needs to be unique; when there are several copies of the same cache the device may not show any of them...
It's a bit old but maybe this thread will help, particularly from post #12:
https://forums.garmin.com/showthread.php?34669-maximum-number-of-waypoints-in-4-1-1/page2
Improving XML handling so we don't choke on large gpx files is on the to-do-list.